Tsuyoshi Ito
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 Apr2 awarded Tag Editor Apr2 revised graph-theory wiki description linked to tag:graph to explain that it is different from this tag Apr2 suggested approved edit on graph-theory tag wiki Mar27 comment How is the graph coloring problem NP-Complete? You are talking about coloring of a planar graph, but strictly speaking, the question is about coloring of a general graph. Mar16 comment A non-distinct system of representative edges. @utdiscant: I prefer your terminology, but some people prefer to treat an edge of a graph as a set of two vertices, in which case the wording of the question is fine. Mar11 comment Knapsack with non-trivial “utility” function In the standard Knapsack problem, only single copy of each item is available. You are probably talking about a variation of the NP-hard problem called the unbounded Knapsack problem. Please check the Wikipedia article which you linked to. Mar10 comment P or NP-Complete? (concerning 2-CNF formulas) @J.D.: cs.stackexchange.com is currently in private beta. Feb29 awarded Enlightened Feb29 awarded Nice Answer Feb24 comment Properties of a valid DFA @CamMcLeman: The word “equivalent” in your comment has to be interpreted with caution, because people care about the difference between, say, DFA and NFA, although they are fairly easily proven “equivalent” under some standard terminology. Feb19 comment The Average Running Time Of Euclid Algorithm? What do you mean by “define it in the limit”? Feb19 comment No identical rectangles in a matrix There is an $O(N^2 M \log M)$-time algorithm. (Hint: First consider the case of a 2×M matrix.) I do not know if there is a faster one. Feb16 comment 1/3+2/3 in double precision In general, if you cannot be sure of the correctness of your own calculation, one of the good ways to check the correctness is by writing down steps more carefully. In your case, the first step is to represent 1/3 and 2/3 as double-precision floating-point numbers. Feb16 comment How can I create/modify 3-SAT functions according to Valiant-Varizani? (1) If you do not understand the proof, then do not say “it’s fairly straightforward.” It may seem cool to say that, but it gives a wrong impression that you believe that you have understood the proof. (2) First, forget Boolean formulas (let alone 3CNF formulas) and understand the algorithm which computes h(x) in the lecture note. It is straightforward, but you cannot go forward without understanding that part. After that, convert the algorithm to a 3CNF formula, either by making some observations about the algorithm or by using the reduction in the Cook-Levin theorem. Feb16 comment How can I create/modify 3-SAT functions according to Valiant-Varizani? Judging from the last paragraph, I doubt that you understand the proof of Valiant-Vazirani, in particular the use of pairwise independent family of hash functions in the proof. Feb15 comment The Average Running Time Of Euclid Algorithm? For every d, there are infinitely many pairs (m,n) such that gcd(m,n)=d. How do you define the average? Feb15 answered if P=NP, then is E=NE? Feb12 answered Different solutions under distributive and commutative equivalence Feb12 comment Different solutions under distributive and commutative equivalence @Rik: Yes, append any two numbers and operators + and / to the formulas I showed, such as (((3−2)×6)+12)/9 and (((6−3)×2)+12)/9. Feb12 comment Different solutions under distributive and commutative equivalence @RikPoggi: If that is the question, then you should have asked it. It is much simpler than the current question. The answer is no. Consider two formulas (3−2)×6=6 and (6−3)×2=6. If we forget the numbers and just consider them as (x−y)×z and (z−x)×y, they are not equivalent. They happen to be equal because of the particular choice of the numbers.