By John E. Hopcroft (auth.), Kun-Mao Chao, Tsan-sheng Hsu, Der-Tsai Lee (eds.)

This booklet constitutes the refereed court cases of the twenty third overseas Symposium on Algorithms and Computation, ISAAC 2012, held in Taipei, Taiwan, in December 2012. The sixty eight revised complete papers offered including 3 invited talks have been rigorously reviewed and chosen from 174 submissions for inclusion within the ebook. This quantity includes issues corresponding to graph algorithms; on-line and streaming algorithms; combinatorial optimization; computational complexity; computational geometry; string algorithms; approximation algorithms; graph drawing; facts constructions; randomized algorithms; and algorithmic online game theory.

**Read or Download Algorithms and Computation: 23rd International Symposium, ISAAC 2012, Taipei, Taiwan, December 19-21, 2012. Proceedings PDF**

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**Additional resources for Algorithms and Computation: 23rd International Symposium, ISAAC 2012, Taipei, Taiwan, December 19-21, 2012. Proceedings**

**Example text**

Xn } and a set of literal clauses {C1 , . . , Cm } over X with the following properties. Each Ci contains either 2 or 3 literals, and these literals are all positive. Moreover, each literal occurs in at most three diﬀerent clauses. One can prove that NotAll-Equal (≤ 3, 2/3)-Satisfiability is NP-complete by a reduction from Not-All-Equal-3-Satisfiability via a well-known folklore trick. Let I be an arbitrary instance of Not-All-Equal (≤ 3, 2/3)-Satisfiability with positive literals. We let x1 , x2 , .

A. Golovach, D. Paulusma, and J. Song Not-All-Equal (≤ 3, 2/3)-Satisfiability with positive literals. The NotAll-Equal 3-Satisfiability problem is NP-complete [18] and is deﬁned as follows. , Cm } of three-literal clauses over X in which all literals are positive, does there exist a truth assignment for X such that each clause contains at least one true literal and at least one false literal? The variant Not-AllEqual (≤ 3, 2/3)-Satisfiability with positive literals asks the same question but takes as input an instance I that has a set of variables {x1 , .

For each node v of G, let N (v) consist of the neighbors of v in G. For each node subset S of G, let N (S) = v∈S N (v). Let Δ = maxv∈V |N (v)|. Let k be a positive integer. Let K = {1, 2, . . , k}. A k-coloring of G is a mapping from V to a color in K such that any two adjacent nodes of G map to diﬀerent colors. Let Ω consist of all k-colorings of G. Markov Chain Monte Carlo is an important tool in sampling from complex distributions such as the uniform distribution on k-coloring. It has been successfully applied in several areas of Computer Science and more details can be found in Frieze and Vigoda [6].