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

ISBN-10: 364235260X

ISBN-13: 9783642352607

This e-book 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 awarded including 3 invited talks have been rigorously reviewed and chosen from 174 submissions for inclusion within the ebook. This quantity comprises themes equivalent 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 video game theory.

**Read Online 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**

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 , . . , 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.

We ﬁrst prove how to transform (G, k, cW ) in polynomial time into a new instance (G , k , cW ) with the following properties: (i) G is a 3P1 -free subgraph of G, k ≤ k and cW : W → {1, . . , k} for some W ⊆ W ⊆ V (G) is a precoloring; (ii) (G , k , cW ) is a yes-instance if and only if (G, k, cW ) is a yes-instance. Suppose that G is not 3P1 -free already. Then G contains at least one triple T of three independent vertices. Let u ∈ T . Here we make the following choice if possible: if there exists a triple of three independent vertices that intersects with W , then we choose T to be such a triple and pick u ∈ T ∩ W .

Recent research eﬀorts focus on the important case that Δ ≥ d log2 n holds for some suﬃciently large constant d. We add the following new results along this direction, where can be any constant with 0 < < 1. 645 be the root of (1 − e−1/x )2 + 2xe−1/x = 2. If G is regular and bipartite and k ≥ (α + )Δ, then the mixing time of the Glauber dynamics for G is O(n log n). 763 be the root of x = e1/x . 5 neighbors for any two adjacent nodes of G is at most 360eΔ and k ≥ (1 + )βΔ, then the mixing time of the Glauber dynamics is O(n log n).