Download Frontiers in Algorithmics: 8th International Workshop, FAW by Jianer Chen, John E. Hopcroft, Jianxin Wang PDF

By Jianer Chen, John E. Hopcroft, Jianxin Wang

This e-book constitutes the refereed lawsuits of the eighth overseas Frontiers of Algorithmics Workshop, FAW 2013, held in Zhangjiajie, China, in June 2014. The 30 revised complete papers awarded including 2 invited talks have been conscientiously reviewed and chosen from sixty five submissions. they supply a concentrated discussion board on present developments of study on algorithms, discrete buildings, operations learn, combinatorial optimization and their applications.

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Extra resources for Frontiers in Algorithmics: 8th International Workshop, FAW 2014, Zhangjiajie, China, June 28-30, 2014. Proceedings

Example text

4, which is separated into three statements, the first of which considers the case when (G) is not chordal. Lemma 9. Given a hole C of (G), we can in O(n + m) time find a minimal forbidden induced subgraph of G. Proof. Let us first take care of some trivial cases. If C is contained in L or R or T , then by construction, φ(C) is a hole of G. This hole is either nonadjacent or completely adjacent to h0 in G, whereupon we can return φ(C) + h0 as a C ∗ or wheel respectively. Since L and R are nonadjacent, it must be one of the cases above if C is disjoint from T .

2. We can call Lem. 2 with x3 and x4 if first(φ(x3 )) = a. In the remaining case, first(φ(x3 )) = a − 1. Let x be the first vertex in P that is adjacent to ha−2 (or hla−2 if a ≤ 3); its existence is clear as x1 satisfies this condition. Then φ({x3 , . . , x, ha−2 , x1 , x2 }) induces a hole of G, and we can return it and ha−1 as a wheel. Assume now that ha is not in C. Denote by P the (x2 , x1 )-path obtained from C by deleting the edge x1 x2 . Let x be the first neighbor of ha+1 in P , and let y be either the first neighbor of ha−1 in the (x, x1 )-path or the other neighbor of x1 in C.

This objective yields the following abstract problem: LINE-MERGING MINIMIZING AFFECTED LINES (LMAL) Input: M ∈ {0, 1}n×m, k ∈ IN. Question: Is there a set S of operations to transform M into a zero matrix with |{li : ((li−1 , li ) ∈ S) ∨ ((li , li+1 ) ∈ S)}| ≤ k? A Fixed-Parameter Approach for Privacy-Protection with Global Recoding 27 A solution for LMAL can also be described by the set of affected lines. A set of lines L will be called feasible, if (li−1 ∈ L) ∨ (li+1 ∈ L) ∀ li ∈ L. A feasible set of lines L is a solution for a LMAL instance (M, k), if the merging-set S = {(li , li+1 ): li , li+1 ∈ L} transforms M into a zero matrix.

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