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In [[applied mathematics]], '''Graver bases''' enable iterative solutions of linear and various nonlinear [[integer programming]] problems in [[polynomial time]]. They were introduced by [[Jack E. Graver]].<ref name="Gra">Jack E. Graver: On the foundations of linear and linear integer programming, Mathematical Programming 9:207–226, 1975</ref> Their connection to the theory of [[Gröbner basis|Gröbner bases]] was discussed by [[Bernd Sturmfels]].<ref name="Stu">[[Bernd Sturmfels]], ''Gröbner Bases and Convex Polytopes'', [[American Mathematical Society]], xii+162 pp., 1996</ref> The algorithmic theory of Graver bases and its application to integer programming is described by [[Shmuel Onn]].<ref name="Onn">[http://ie.technion.ac.il/~onn Shmuel onn]: [http://books.google.co.il/books?id=yXvfDzHo-WsC&printsec=frontcover&dq=inauthor:%22Shmuel+Onn%22&hl=en&ei=ccjLToGAPMXLhAep-ZznDQ&sa=X&oi=book_result&ct=result&redir_esc=y#v=onepage&q=inauthor%3A%22Shmuel%20Onn%22&f=false ''Nonlinear Discrete Optimization''], [[European Mathematical Society]], x+137 pp., 2010</ref><ref name="MSRI">Shmuel Onn: [http://www.msri.org/web/msri/online-videos/-/video/showSpeaker/200002593 Linear and nonlinear integer optimization], Online Video Lecture Series, [[Mathematical Sciences Research Institute]], Berkeley, 2010</ref>
Four or five years ago, a reader of some of my columns bought the domain name jamesaltucher.com and gave it to me as a birthday gift. It was a total surprise to me. I didn't even know the reader. I hope one day we meet.<br>Two years ago a friend of mine, Tim Sykes, insisted I had to have a blog. He set it up for me. He even wrote the "About Me". I didn't want a blog. I had nothing to say. But about 6 or 7 months ago I decided I wanted to take this blog seriously. I kept putting off changing the "About Me" which was no longer really about me and maybe never was.<br>A few weeks ago I did a chapter in one of the books in Seth Godin's "The Domino Project". The book is out and called "No Idling". Mohit Pewar organized it (here's Mohit's blog) and sent me a bunch of questions recently. It's intended to be an interview on his blog but I hope Mohit forgives me because I want to use it as my new "About Me" also.<br>1. You are a trader, investor, writer, and entrepreneur? Which of these roles you enjoy the most and why?<br>When I first moved to New York City in 1994 I wanted to be everything to everyone. I had spent the six years prior to that writing a bunch of unpublished novels and unpublished short stories. I must've sent out 100s of stories to literary journals. I got form rejections from every publisher, journal, and agent I sent my novels and stories to.<br>Now, in 1994, everything was possible. The money was in NYC. Media was here. I lived in my 10�10 room and pulled suits out of a garbage bag every morning but it didn't matter...the internet was revving up and I knew how to build a website. One of the few in the city. My sister warned me though: nobody here is your friend. Everybody wants something<br>
And I wanted something. I wanted the [http://search.un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=fleeting+feelings&Submit=Go fleeting feelings] of success, for the first time ever, in order to feel better about myself. I wanted a girl next to me. I wanted to build and sell companies and finally prove to everyone I was the smartest. I wanted to do a TV show. I wanted to write books<br>
But everything involved having a master. Clients. Employers. Investors. Publishers. The market (the deadliest master of all). Employees. I was a slave to everyone for so many years. And the more shackles I had on, the lonelier I got<br>
Much of the time, even when I had those moments of success, I didn't know how to turn it into a better life. I felt ugly and then later, I felt stupid when I would let the success dribble away down the sink<br>
I love writing because every now and then that ugliness turns into honesty. When I write, I'm only a slave to myself. When I do all of those other things you ask about, I'm a slave to everyone else<br>
Some links<br>
33 Unusual Tips to Being a Better Write<br>
"The Tooth<br>
(one of my favorite posts on my blog<br>
2. What inspires you to get up and start working/writing every day<br>
The other day I had breakfast with a fascinating guy who had just sold a piece of his fund of funds. He told me what "fracking" was and how the US was going to be a major oil player again. We spoke for two hours about a wide range of topics, including what happens when we can finally implant a google chip in our brains<br>
After that I had to go onto NPR because I firmly believe that in one important respect we are degenerating as a country - we are graduating a generation of indentured servants who will spend 50 years or more paying down their student debt rather than starting companies and curing cancer. So maybe I made a difference<br>
Then I had lunch with a guy I hadn't seen in ten years. In those ten years he had gone to jail and now I was finally taking the time to forgive him for something he never did to me. I felt bad I hadn't helped him when he was at his low point. Then I came home and watched my kid play clarinet at her school. Then I read until I fell asleep. Today I did nothing but write. Both days inspired me<br>
It also inspires me that I'm being asked these questions. Whenever anyone asks me to do anything I'm infinitely grateful. Why me? I feel lucky. I like it when someone cares what I think. I'll write and do things as long as anyone cares. I honestly probably wouldn't write if nobody cared. I don't have enough humility for that, I'm ashamed to admit<br>
3. Your new book "How to be the luckiest person alive" has just come out. What is it about<br>
When I was a kid I thought I needed certain things: a college education from a great school, a great home, a lot of money, someone who would love me with ease. I wanted people to think I was smart. I wanted people to think I was even special.  And as I grew older more and more goals got added to the list: a high chess rating, a published book, perfect weather, good friends,  respect in various fields, etc. I lied to myself that I needed these things to be happy. The world was going to work hard to give me these things, I thought. But it turned out the world owed me no favors<br>
And gradually, over time, I lost everything I had ever gained. Several times.  I've paced at night so many times wondering what the hell was I going to do next or trying not to care. The book is about regaining your sanity, regaining your happiness, finding luck in all the little pockets of life that people forget about. It's about turning away from the religion you've been hypnotized into believing into the religion you can find inside yourself every moment of the day<br>
[Note: in a few days I'm going to do a post on self-publishing and also how to get the ebook for free. The link above is to the paperback. Kindle should be ready soon also.<br>
Related link: Why I Write Books Even Though I've Lost Money On Every Book I've Ever Writte<br>
4. Is it possible to accelerate success? If yes, how<br>
Yes, and it's the only way I know actually to achieve success. It's by following the Daily Practice I outline in this post:<br>
It's the only way I know to exercise every muscle from the inside of you to the outside of you. I firmly believe that happiness starts with that practice<br>
5. You say that discipline, persistence and psychology are important if one has to achieve success. How can one work on improving "psychology" part<br>
Success doesn't really mean anything. People want to be happy in a harsh and unforgiving world. It's very difficult. We're so lucky most of us live in countries without major wars. Our kids aren't getting killed by random gunfire. We all have cell phones. We all can communicate with each other on the Internet. We have Google to catalog every piece of information in history!  We are so amazingly lucky already<br>
How can it be I was so lucky to be born into such a body? In New York City of all places? Just by being born in such a way on this planet was an amazing success<br>
So what else is there? The fact is that most of us, including me, have a hard time being happy with such ready-made success. We quickly adapt and want so much more out of life. It's not wars or disease that kill us. It's the minor inconveniences that add up in life. It's the times we feel slighted or betrayed. Or even slightly betrayed. Or overcharged. Or we miss a train. Or it's raining today. Or the dishwasher doesn't work. Or the supermarket doesn't have the food we like. We forget how good the snow tasted when we were kids. Now we want gourmet food at every meal<br>
Taking a step back, doing the Daily Practice I outline in the question above. For me, the results of that bring me happiness. That's success. Today. And hopefully tomorrow<br>
6. You advocate not sending kids to college. What if kids grow up and then blame their parents about not letting them get a college education<br>
I went to one of my kid's music recitals yesterday. She was happy to see me. I hugged her afterwards. She played "the star wars theme" on the clarinet. I wish I could've played that for my parents. My other daughter has a dance recital in a few weeks. I tried to give her tips but she laughed at me. I was quite the breakdancer in my youth. The nerdiest breakdancer on the planet. I want to be present for them. To love them. To let them always know that in their own dark moments, they know I will listen to them. I love them. Even when they cry and don't always agree with me. Even when they laugh at me because sometimes I act like a clown<br>
Later, if they want to blame me for anything at all then I will still love them. That's my "what if"<br>
Two posts<br>
I want my daughters to be lesbian<br>
Advice I want to give my daughter<br><br>


==Formal definition==


The '''Graver basis''' of an ''m''&nbsp;&times;&nbsp;''n'' integer matrix <math>A</math> is the finite set <math>G(A)</math> of minimal elements in the set
7. Four of your favorite posts from The Altucher Confidential<br>
 
As soon as I publish a post I get scared to death. Is it good? Will people re-tweet? Will one part of the audience of this blog like it at the expense of another part of the audience. Will I get Facebook Likes? I have to stop clinging to these things but you also need to respect the audience. I don't know. It's a little bit confusing to me. I don't have the confidence of a real writer yet<br>
: <math>\{x\in\mathbb{Z}^n : Ax=0,\ x\neq 0\} \, </math>
Here are four of my favorites<br>
 
How I screwed Yasser Arafat out of $2mm (and lost another $100mm in the process<br>
under a well partial order on <math>\mathbb{Z}^n</math> defined by <math>x\sqsubseteq y</math> when <math>x_iy_i\geq 0</math> and <math>|x_i|\leq |y_i|</math> for all i. For example, the Graver basis of <math>A=(1 2 1)</math> consists of the vectors (2,&minus;1,0), (0,&minus;1,2), (1,0,&minus;1), (1,&minus;1,1) and their negations.
It's Your Fault<br>
 
I'm Guilty of Torturing Wome<br>
==Solving integer programming using Graver bases==
The Girl Whose Name Was a Curs<br>
 
Although these three are favorites I really don't post anything unless it's my favorite of that moment<br>
[[Integer programming]] is the problem of optimizing a linear or nonlinear objective function over the set of integer points satisfying a system of linear inequalities. Formally, it can be written in standard form as follows:
8. 3 must-read books for aspiring entrepreneurs<br>
 
The key in an entrepreneur book: you want to learn business. You want to learn how to honestly communicate with your customers. You want to stand out<br>
:<math>\min\{f(x)\ :\ x \in \mathbb{Z}^n,\ Ax=b,\ l\leq x\leq u\}\ .</math>
The Essays of Warren Buffett by Lawrence Cunningha<br>
 
"The Thank you Economy" by Gary Vaynerchu<br>
It is one of the most fundamental discrete optimization problems and has a very broad modeling power and numerous applications in a variety of areas, but is typically very hard computationally as noted below. However, given the Graver basis <math>G(A)</math> of <math>A</math>, the problem with linear and various nonlinear objective functions can be solved in polynomial time as explained next.
"Purple cow" by Seth Godi<br>
 
9. I love your writing, so do so many others out there. Who are your favorite writers<br>
===Linear integer programming===
"Jesus's Son" by Denis Johnson is the best collection of short stories ever written. I'm afraid I really don't like his novels though<br>
 
"Tangents" by M. Prado. A beautiful series of graphic stories about relationships<br>
The most studied case, treated thoroughly in,<ref name="Sch">[[Alexander Schrijver]]: ''Theory of Linear and Integer Programming'', Wiley, xii+471 pp., 1986</ref> is that of [[integer programming|linear integer programming]],
Other writers: Miranda July, Ariel Leve, Mary Gaitskill, Charles Bukowski, [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine UK], Sam Lipsyte, William Vollmann, Raymond Carver. Arthur Nersesian. Stephen Dubner<br>
 
Many writers are only really good storytellers. Most writers come out of a cardboard factory MFA system and lack a real voice. A real voice is where every word exposes ten levels of hypocrisy in the world and brings us all the way back to see reality. The writers above have their own voices, their own pains, and their unique ways of expressing those pains. Some of them are funny. Some a little more dark. I wish I could write 1/10 as good as any of them<br><br>
:<math>\min\{wx\ :\ x \in \mathbb{Z}^n,\ Ax=b,\ l\leq x\leq u\}\ .</math>
10. You are a prolific writer. Do you have any hacks that help you write a lot in little time<br>
 
Coffee, plus everything else coffee does for you first thing in the morning<br>
It may be assumed that all variables are bounded from below and above: such bounds either appear naturally in the application at hand, or can be enforced without losing any optimal solutions. But, even with linear objective functions the problem is NP-hard and hence presumably cannot be solved in polynomial time.
Only write about things you either love or hate. But if you hate something, try to find a tiny gem buried in the bag of dirt so you can reach in when nobody is looking and put that gem in your pocket. Stealing a diamond in all the shit around us and then giving it away for free via writing is a nice little hack, Being fearless precisely when you are most scared is the best hack<br><br>
 
11. I totally get and love your idea about bleeding as a writer, appreciate if you share more with the readers of this blog<br>
However, given the Graver basis <math>G(A)</math> of <math>A</math> it ''can'' be solved in polynomial time using the following simple iterative algorithm.<ref name="Onn" /><ref name="HOW">Raymond Hemmecke, Shmuel Onn, Robert Weismantel: A polynomial oracle-time
Most people worry about what other people think of them. Most people worry about their health. Most people are at a crossroads and don't know how to take the next step and which road to take it on. Everyone is in a perpetual state of 'where do I put my foot next'. Nobody, including me, can avoid that<br>
algorithm for convex integer minimization, Mathematical Programming
You and I both need to wash our faces in the morning, brush our teeth, shower, shit, eat, fight the weather, fight the colds that want to attack us if we're not ready. Fight loneliness or learn how to love and appreciate the people who want to love you back. And learn how to forgive and love the people who are even more stupid and cruel than we are. We're afraid to tell each other these things because they are all both disgusting and true<br>
126:97–117, 2011</ref> Assume first that some initial feasible point ''x'' is given. While possible, repeat the following iteration: find positive integer ''q'' and element ''g'' in <math>G(A)</math> such that ''x''&nbsp;+&nbsp;''qg'' does not violate the bounds and gives best possible improvement; update ''x''&nbsp;:=&nbsp;''x''&nbsp;+&nbsp;''qg'' and proceed to the next iteration. The last point ''x'' is optimal and the number of iterations is polynomial. To find an initial feasible point, a suitable auxiliary program can be set up and solved in a similar fashion.
You and I both have the same color blood. If I cut my wrist open you can see the color of my blood. You look at it and see that it's the same color as yours. We have something in common. It doesn't have to be shameful. It's just red. Now we're friends. No matter whom you are or where you are from. I didn't have to lie to you to get you to be my friend<br>
 
Related Links<br>
===Nonlinear integer programming===
How to be a Psychic in Ten Easy Lesson<br>
 
My New Year's Resolution in 199<br>
Turning to the case of general objective functions ''f'', if the variables are unbounded then the problem may in fact be uncomputable: it follows from the solution of [[Hilbert's 10th problem]] (see <ref name="Mat">Yuri V. Matiyasevich: ''Hilbert's Tenth Problem'', MIT Press, xxiv+264 pp., 1993</ref>), that there exists no algorithm which, given an integer polynomial ''f'' of degree 8 in 58 variables, decides if the minimum value of f over all 58-dimensional integer vectors is 0. However, when the variables are bounded, the problem
12. What is your advice for young entrepreneurs<br>
 
Only build something you really want to use yourself. There's got to be one thing you are completely desperate for and no matter where you look you can't find it. Nobody has invented it yet. So there you go - you invent it. If there's other people like you, you have a business. Else. You fail. Then do it again. Until it works. One day it will<br>
: <math>\min\{f(x)\ :\ x \in \mathbb{Z}^n,\ Ax=b,\ l\leq x\leq u\}</math>
Follow these 100 Rules<br>
 
The 100 Rules for Being a Good Entrepreneur<br>
can be solved using the Graver basis <math>G(A)</math> in polynomial time for
And, in particular this<br>
several nonlinear objective functions including:
The Easiest Way to Succeed as an Entrepreneu<br>
 
In my just released book I have more chapters on my experiences as an entrepreneur<br>
* '''Separable-convex''' functions of the form <math>f(x)=\sum_{i=1}^n f_i(x_i)</math>;
13. I advocate the concept of working at a job while building your business. You have of course lived it. Now as you look back, what is your take on this? Is it possible to make it work while sailing on two boats<br><br>
* In particular the '''p-norm''' <math>f(x)=\|x\|_p</math> for every positive integer ''p'';
Your boss wants everything out of you. He wants you to work 80 hours a week. He wants to look good taking credit for your work. He wants your infinite loyalty. So you need something back<br>
* '''Composite-concave''' functions ''f''(''x'')&nbsp;=&nbsp;''g''(''Wx''), where ''W'' is a ''d''&nbsp;&times;&nbsp;''n'' integer matrix with ''d'' fixed, and where ''g'' is a ''d''-variate concave function;
Exploit your employer. It's the best way to get good experience, clients, contacts. It's a legal way to steal. It's a fast way to be an entrepreneur because you see what large companies with infinite money are willing to pay for. If you can provide that, you make millions. It's how many great businesses have started and will always start. It's how every exit I've had started<br><br>
* Certain '''(in)-definite quadratic''' and '''higher degree polynomial''' functions.
14. Who is a "person with true moral fiber"? In current times are there any role models who are people with true moral fiber<br>
 
I don't really know the answer. I think I know a few people like that. I hope I'm someone like that. And I pray to god the people I'm invested in are like that and my family is like that<br>
==Some applications==
I find most people to be largely mean and stupid, a vile combination. It's not that I'm pessimistic or cynical. I'm very much an optimist. It's just reality. Open the newspaper or turn on the TV and watch these people<br>
 
Moral fiber atrophies more quickly than any muscle on the body. An exercise I do every morning is to promise myself that "I'm going to save a life today" and then leave it in the hands of the Universe to direct me how I can best do that. Through that little exercise plus the Daily Practice described above I hope to keep regenerating that fiber<br>
===Multi-dimensional tables===
15.  Your message to the readers of this blog<br>
 
Skip dinner. But follow me on Twitter.<br>
Consider the following optimization problem over three-dimensional tables with prescribed line sums,
Read more posts on The Altucher Confidential �
 
More from The Altucher Confidentia<br>
:<math>\min\{wx\ :\ x\in{\mathbb{Z}}_+^{l\times m\times n}\,,\ \sum_i x_{i,j,k}=a_{j,k} \,,\ \sum_j x_{i,j,k}=b_{i,k}\,,\ \sum_k x_{i,j,k}=c_{i,j}\}\ ,</math>
Life is Like a Game. Here�s How You Master ANY Gam<br><br>
 
Step By Step Guide to Make $10 Million And Then Totally Blow <br><br>
with <math>a_{j,k}</math>, <math>b_{i,k}</math>, <math>c_{i,j}</math> nonnegative integers (whose maximum value implicitly bounds all variables from above). Denote by <math>A</math> the (''lm''&nbsp;+&nbsp;''ln''&nbsp;+&nbsp;''mn'')&nbsp;&times;&nbsp;(''lmn'') defining matrix of this system. Note that this matrix is generally ''not'' [[totally unimodular]]. Nonetheless, it was shown in <ref name="DHOW">Jesus A. De Loera, Raymond Hemmecke, Shmuel Onn, Robert Weismantel: ''N''-fold integer programming, Discrete
Can You Do One Page a Day?
Optimization, 5:231–241, 2008</ref> that for every fixed ''l'' and ''m'', its Graver basis <math>G(A)</math> can be computed in time which is polynomial in&nbsp;''n''. The results mentioned above allow then to solve this problem in polynomial time for fixed ''l'' and ''m'' and variable ''n''. Note that if only one side ''l'' of the table is fixed (even with ''l''&nbsp;=&nbsp;3) while both ''m'' and ''n'' are variable, then the problem is NP hard, as shown in.<ref name="DO1">Jesus A. De Loera, Shmuel Onn: The complexity of
three-way statistical tables, SIAM Journal on Computing, 33:819–836, 2004</ref> More generally, similar positive results hold for higher dimensional table problems (introduced in <ref name="Mot">Theodore S. Motzkin: The multi-index transportation
problem, Bulletin of the American Mathematical Society 58:494, 1952</ref>): for every fixed ''d'' and <math>m_1, \dots, m_d</math>, (non)-linear optimization over <math>m_1 \times \cdots \times m_d \times n</math> tables with variable n and prescribed margins can be done in polynomial time. This has further applications to entry security problems and privacy in statistical databases.
 
===Multi-commodity flows===
 
Consider the ''integer'' [[multi-commodity flow problem]] of routing ''k'' types of integer commodities from ''m'' suppliers to ''n'' consumers subject to supply, consumption, and capacity constraints, so as to minimize the sum of linear or congestion-dependent convex costs on the arcs. Then for every fixed ''k'' and ''m'', the Graver basis of the defining system can be computed and the resulting separable-convex objective function
minimized in time which is polynomial in the variable number ''n'' of consumers and in the rest of the data.
 
===Other applications===
 
The many applications of the algorithmic theory of Graver bases also include stochastic integer programming,<ref name="HOW" /> ''N''-fold integer programming, ''N''-fold 4-block decomposable integer programming,<ref name="HKW">Raymond Hemmecke, Matthias Köppe, Robert Weismantel: A polynomial-time algorithm for optimizing over ''N''-fold 4-block decomposable integer programs, IPCO 14, 2010</ref> clustering, and disclosure control in statistical databases. In some of these applications the relevant Graver basis ''cannot'' be computed in polynomial time, but can be accessed in an indirect way that allows to use it in polynomial time.
 
==Universality and parametrization==
 
It was shown in <ref name="DO2">Jesus A. De Loera, Shmuel Onn: All
linear and integer programs are slim 3-way transportation programs, SIAM Journal on Optimization, 17:806–821, 2006</ref> that every (bounded) integer programming problem is precisely equivalent to the 3&nbsp;&times;&nbsp;''m''&nbsp;&times;&nbsp;''n'' table problem discussed above for some ''m'' and ''n'' and some line sums. Thus, such 3&nbsp;&times;&nbsp;''m''&nbsp;&times;&nbsp;''n'' table problems are '''universal''' for integer programming. Moreover, for each fixed ''m'', the resulting class of integer programs can be solved in polynomial time by the iterative Graver basis method described above. So the table width ''m'' provides a '''parametrization''' of all integer programming problems.
 
==Hierarchy of approximations for integer programming==
 
Denote by <math>G(m,n)</math> the Graver basis of the matrix <math>A</math> defining the universal 3&nbsp;&times;&nbsp;''m''&nbsp;&times;&nbsp;''n'' table problem discussed above. The elements of <math>G(m,n)</math> are 3&nbsp;&times;&nbsp;''m''&nbsp;&times;&nbsp;''n'' tables with all line sums equal to 0. The ''type'' of such a table is the number of its nonzero 3&nbsp;&times;&nbsp;''m'' ''layers''. It turns out that there is a finite ''Graver complexity function'' ''g''(''m'') such that for any ''n'', the type of any element of the Graver basis <math>G(m,n)</math> is at most ''g''(''m''). It follows that the Graver basis <math>G(m,n)</math> is the union of the <math>{n\choose g(m)}</math> suitably embedded copies of the Graver basis <math>G(m,g(m))</math>. To approximately solve in practice an arbitrary integer programming problem, proceed as follows. First embed it in a suitable 3&nbsp;&times;&nbsp;''m''&nbsp;&times;&nbsp;''n'' table problem as enabled by the universality noted above. Now apply the following hierarchy of approximations of <math>G(m,n)</math>. At level ''k'' of this hierarchy, let <math>G_k(m,n)</math> be the subset of <math>G(m,n)</math> consisting only of those elements of type at most ''k''; use this approximation <math>G_k(m,n)</math> in the iterative algorithm as long as possible to obtain as good as possible feasible point for the integer programming problem embedded in the 3&nbsp;&times;&nbsp;''m''&nbsp;&times;&nbsp;''n'' table problem; if the objective function value of this point is satisfactory (say, as compared to the value of the [[linear programming relaxation]]), then use this point; otherwise increment ''k'' and proceed to the next level of the hierarchy. It can be shown <ref name="Onn" /> that for any fixed level ''k'', the approximation <math>G_k(m,n)</math> of the Graver basis has polynomial cardinality <math>O\left(m^{g(k)}n^k\right)</math> and can be computed in that much time.
 
==Fixed parameter tractability: from polynomial to cubic time complexity==
 
The time complexity of solving some of the applications discussed above, such as multi-dimensional table problems, multicommodity flow problems, and ''N''-fold integer programming problems, is dominated by the cardinality of the relevant Graver basis, which is a polynomial <math>O\left(n^g\right)</math> with typically large degree ''g'' which
is a suitable Graver complexity of the system. In <ref name="HOR">Raymond Hemmecke, Shmuel Onn, Lyubov Romanchuk: ''N''-fold integer programming in cubic time, Mathematical Programming, 137:325–341, 2013</ref> a much faster algorithm is presented, which finds at each iteration the best improvement ''x''&nbsp;+&nbsp;''qg'' with ''q'' positive integer and ''g'' element in <math>G(A)</math> ''without explicitly constructing the Graver basis'', in cubic time <math>O\left(n^3\right)</math> regardless of the system.
In the terminology of [[parameterized complexity]], this implies that all these problems suitably parameterized, and in particular ''l''&nbsp;&times;&nbsp;''m''&nbsp;&times;&nbsp;''n'' table problems parametrized by ''l'' and ''m'', are '''fixed parameter tractable'''.
 
==References==
 
{{reflist}}
 
[[Category:Linear programming]]

Latest revision as of 13:19, 21 May 2014

Four or five years ago, a reader of some of my columns bought the domain name jamesaltucher.com and gave it to me as a birthday gift. It was a total surprise to me. I didn't even know the reader. I hope one day we meet.
Two years ago a friend of mine, Tim Sykes, insisted I had to have a blog. He set it up for me. He even wrote the "About Me". I didn't want a blog. I had nothing to say. But about 6 or 7 months ago I decided I wanted to take this blog seriously. I kept putting off changing the "About Me" which was no longer really about me and maybe never was.
A few weeks ago I did a chapter in one of the books in Seth Godin's "The Domino Project". The book is out and called "No Idling". Mohit Pewar organized it (here's Mohit's blog) and sent me a bunch of questions recently. It's intended to be an interview on his blog but I hope Mohit forgives me because I want to use it as my new "About Me" also.
1. You are a trader, investor, writer, and entrepreneur? Which of these roles you enjoy the most and why?
When I first moved to New York City in 1994 I wanted to be everything to everyone. I had spent the six years prior to that writing a bunch of unpublished novels and unpublished short stories. I must've sent out 100s of stories to literary journals. I got form rejections from every publisher, journal, and agent I sent my novels and stories to.
Now, in 1994, everything was possible. The money was in NYC. Media was here. I lived in my 10�10 room and pulled suits out of a garbage bag every morning but it didn't matter...the internet was revving up and I knew how to build a website. One of the few in the city. My sister warned me though: nobody here is your friend. Everybody wants something
And I wanted something. I wanted the fleeting feelings of success, for the first time ever, in order to feel better about myself. I wanted a girl next to me. I wanted to build and sell companies and finally prove to everyone I was the smartest. I wanted to do a TV show. I wanted to write books
But everything involved having a master. Clients. Employers. Investors. Publishers. The market (the deadliest master of all). Employees. I was a slave to everyone for so many years. And the more shackles I had on, the lonelier I got
Much of the time, even when I had those moments of success, I didn't know how to turn it into a better life. I felt ugly and then later, I felt stupid when I would let the success dribble away down the sink
I love writing because every now and then that ugliness turns into honesty. When I write, I'm only a slave to myself. When I do all of those other things you ask about, I'm a slave to everyone else
Some links
33 Unusual Tips to Being a Better Write
"The Tooth
(one of my favorite posts on my blog
2. What inspires you to get up and start working/writing every day
The other day I had breakfast with a fascinating guy who had just sold a piece of his fund of funds. He told me what "fracking" was and how the US was going to be a major oil player again. We spoke for two hours about a wide range of topics, including what happens when we can finally implant a google chip in our brains
After that I had to go onto NPR because I firmly believe that in one important respect we are degenerating as a country - we are graduating a generation of indentured servants who will spend 50 years or more paying down their student debt rather than starting companies and curing cancer. So maybe I made a difference
Then I had lunch with a guy I hadn't seen in ten years. In those ten years he had gone to jail and now I was finally taking the time to forgive him for something he never did to me. I felt bad I hadn't helped him when he was at his low point. Then I came home and watched my kid play clarinet at her school. Then I read until I fell asleep. Today I did nothing but write. Both days inspired me
It also inspires me that I'm being asked these questions. Whenever anyone asks me to do anything I'm infinitely grateful. Why me? I feel lucky. I like it when someone cares what I think. I'll write and do things as long as anyone cares. I honestly probably wouldn't write if nobody cared. I don't have enough humility for that, I'm ashamed to admit
3. Your new book "How to be the luckiest person alive" has just come out. What is it about
When I was a kid I thought I needed certain things: a college education from a great school, a great home, a lot of money, someone who would love me with ease. I wanted people to think I was smart. I wanted people to think I was even special. And as I grew older more and more goals got added to the list: a high chess rating, a published book, perfect weather, good friends, respect in various fields, etc. I lied to myself that I needed these things to be happy. The world was going to work hard to give me these things, I thought. But it turned out the world owed me no favors
And gradually, over time, I lost everything I had ever gained. Several times. I've paced at night so many times wondering what the hell was I going to do next or trying not to care. The book is about regaining your sanity, regaining your happiness, finding luck in all the little pockets of life that people forget about. It's about turning away from the religion you've been hypnotized into believing into the religion you can find inside yourself every moment of the day
[Note: in a few days I'm going to do a post on self-publishing and also how to get the ebook for free. The link above is to the paperback. Kindle should be ready soon also.
Related link: Why I Write Books Even Though I've Lost Money On Every Book I've Ever Writte
4. Is it possible to accelerate success? If yes, how
Yes, and it's the only way I know actually to achieve success. It's by following the Daily Practice I outline in this post:
It's the only way I know to exercise every muscle from the inside of you to the outside of you. I firmly believe that happiness starts with that practice
5. You say that discipline, persistence and psychology are important if one has to achieve success. How can one work on improving "psychology" part
Success doesn't really mean anything. People want to be happy in a harsh and unforgiving world. It's very difficult. We're so lucky most of us live in countries without major wars. Our kids aren't getting killed by random gunfire. We all have cell phones. We all can communicate with each other on the Internet. We have Google to catalog every piece of information in history! We are so amazingly lucky already
How can it be I was so lucky to be born into such a body? In New York City of all places? Just by being born in such a way on this planet was an amazing success
So what else is there? The fact is that most of us, including me, have a hard time being happy with such ready-made success. We quickly adapt and want so much more out of life. It's not wars or disease that kill us. It's the minor inconveniences that add up in life. It's the times we feel slighted or betrayed. Or even slightly betrayed. Or overcharged. Or we miss a train. Or it's raining today. Or the dishwasher doesn't work. Or the supermarket doesn't have the food we like. We forget how good the snow tasted when we were kids. Now we want gourmet food at every meal
Taking a step back, doing the Daily Practice I outline in the question above. For me, the results of that bring me happiness. That's success. Today. And hopefully tomorrow
6. You advocate not sending kids to college. What if kids grow up and then blame their parents about not letting them get a college education
I went to one of my kid's music recitals yesterday. She was happy to see me. I hugged her afterwards. She played "the star wars theme" on the clarinet. I wish I could've played that for my parents. My other daughter has a dance recital in a few weeks. I tried to give her tips but she laughed at me. I was quite the breakdancer in my youth. The nerdiest breakdancer on the planet. I want to be present for them. To love them. To let them always know that in their own dark moments, they know I will listen to them. I love them. Even when they cry and don't always agree with me. Even when they laugh at me because sometimes I act like a clown
Later, if they want to blame me for anything at all then I will still love them. That's my "what if"
Two posts
I want my daughters to be lesbian
Advice I want to give my daughter


7. Four of your favorite posts from The Altucher Confidential
As soon as I publish a post I get scared to death. Is it good? Will people re-tweet? Will one part of the audience of this blog like it at the expense of another part of the audience. Will I get Facebook Likes? I have to stop clinging to these things but you also need to respect the audience. I don't know. It's a little bit confusing to me. I don't have the confidence of a real writer yet
Here are four of my favorites
How I screwed Yasser Arafat out of $2mm (and lost another $100mm in the process
It's Your Fault
I'm Guilty of Torturing Wome
The Girl Whose Name Was a Curs
Although these three are favorites I really don't post anything unless it's my favorite of that moment
8. 3 must-read books for aspiring entrepreneurs
The key in an entrepreneur book: you want to learn business. You want to learn how to honestly communicate with your customers. You want to stand out
The Essays of Warren Buffett by Lawrence Cunningha
"The Thank you Economy" by Gary Vaynerchu
"Purple cow" by Seth Godi
9. I love your writing, so do so many others out there. Who are your favorite writers
"Jesus's Son" by Denis Johnson is the best collection of short stories ever written. I'm afraid I really don't like his novels though
"Tangents" by M. Prado. A beautiful series of graphic stories about relationships
Other writers: Miranda July, Ariel Leve, Mary Gaitskill, Charles Bukowski, Celine UK, Sam Lipsyte, William Vollmann, Raymond Carver. Arthur Nersesian. Stephen Dubner
Many writers are only really good storytellers. Most writers come out of a cardboard factory MFA system and lack a real voice. A real voice is where every word exposes ten levels of hypocrisy in the world and brings us all the way back to see reality. The writers above have their own voices, their own pains, and their unique ways of expressing those pains. Some of them are funny. Some a little more dark. I wish I could write 1/10 as good as any of them

10. You are a prolific writer. Do you have any hacks that help you write a lot in little time
Coffee, plus everything else coffee does for you first thing in the morning
Only write about things you either love or hate. But if you hate something, try to find a tiny gem buried in the bag of dirt so you can reach in when nobody is looking and put that gem in your pocket. Stealing a diamond in all the shit around us and then giving it away for free via writing is a nice little hack, Being fearless precisely when you are most scared is the best hack

11. I totally get and love your idea about bleeding as a writer, appreciate if you share more with the readers of this blog
Most people worry about what other people think of them. Most people worry about their health. Most people are at a crossroads and don't know how to take the next step and which road to take it on. Everyone is in a perpetual state of 'where do I put my foot next'. Nobody, including me, can avoid that
You and I both need to wash our faces in the morning, brush our teeth, shower, shit, eat, fight the weather, fight the colds that want to attack us if we're not ready. Fight loneliness or learn how to love and appreciate the people who want to love you back. And learn how to forgive and love the people who are even more stupid and cruel than we are. We're afraid to tell each other these things because they are all both disgusting and true
You and I both have the same color blood. If I cut my wrist open you can see the color of my blood. You look at it and see that it's the same color as yours. We have something in common. It doesn't have to be shameful. It's just red. Now we're friends. No matter whom you are or where you are from. I didn't have to lie to you to get you to be my friend
Related Links
How to be a Psychic in Ten Easy Lesson
My New Year's Resolution in 199
12. What is your advice for young entrepreneurs
Only build something you really want to use yourself. There's got to be one thing you are completely desperate for and no matter where you look you can't find it. Nobody has invented it yet. So there you go - you invent it. If there's other people like you, you have a business. Else. You fail. Then do it again. Until it works. One day it will
Follow these 100 Rules
The 100 Rules for Being a Good Entrepreneur
And, in particular this
The Easiest Way to Succeed as an Entrepreneu
In my just released book I have more chapters on my experiences as an entrepreneur
13. I advocate the concept of working at a job while building your business. You have of course lived it. Now as you look back, what is your take on this? Is it possible to make it work while sailing on two boats

Your boss wants everything out of you. He wants you to work 80 hours a week. He wants to look good taking credit for your work. He wants your infinite loyalty. So you need something back
Exploit your employer. It's the best way to get good experience, clients, contacts. It's a legal way to steal. It's a fast way to be an entrepreneur because you see what large companies with infinite money are willing to pay for. If you can provide that, you make millions. It's how many great businesses have started and will always start. It's how every exit I've had started

14. Who is a "person with true moral fiber"? In current times are there any role models who are people with true moral fiber
I don't really know the answer. I think I know a few people like that. I hope I'm someone like that. And I pray to god the people I'm invested in are like that and my family is like that
I find most people to be largely mean and stupid, a vile combination. It's not that I'm pessimistic or cynical. I'm very much an optimist. It's just reality. Open the newspaper or turn on the TV and watch these people
Moral fiber atrophies more quickly than any muscle on the body. An exercise I do every morning is to promise myself that "I'm going to save a life today" and then leave it in the hands of the Universe to direct me how I can best do that. Through that little exercise plus the Daily Practice described above I hope to keep regenerating that fiber
15. Your message to the readers of this blog
Skip dinner. But follow me on Twitter.
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