Download Combinatorial Algorithms: 24th International Workshop, IWOCA by Stefan Edelkamp, Amr Elmasry, Jyrki Katajainen, Armin Weiß PDF

By Stefan Edelkamp, Amr Elmasry, Jyrki Katajainen, Armin Weiß (auth.), Thierry Lecroq, Laurent Mouchard (eds.)

This ebook constitutes the completely refereed post-workshop court cases of the twenty fourth foreign Workshop on Combinatorial Algorithms, IWOCA 2013, held in Rouen, France, in July 2013. The 33 revised complete papers awarded including 10 brief papers and five invited talks have been conscientiously reviewed and chosen from a complete of ninety one submissions. The papers are equipped in topical sections on algorithms on graphs; algorithms on strings; discrete geometry and satisfiability.

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Additional info for Combinatorial Algorithms: 24th International Workshop, IWOCA 2013, Rouen, France, July 10-12, 2013, Revised Selected Papers

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Theorem 4. MR under the Minimum distance F−∞ is NP-complete even for k = 0. Proof. There is a consensus τ ∈ Perm(D) with maxm j=1 minx∈D |σj (x) − τ (x)| = 0 if and only if for every σj there is a candidate x such that σj (x) = τ (x). Then τ hits σj at position τ (x) and we call τ hitting consensus. First we show how to construct an instance with 2n voters of length n which has no hitting consensus. Let D = {u1 , . . , un } and σ1 : D → n : ui → i. We obtain n primary voters σ1 , . . , σn by rotating σ1 , i.

Consider the modification set of Lemma 11. The Hamming distance between two permutations can be computed in linear time. Thus, lines 3, 4 and 6 of Algorithm 1 need O(mn) time. Similarly to the proof of Corollary 3, the iteration of τ over the modification set M (τ, σ) with |M (τ, σ)| ≤ 2k is done in place and needs only O(k) time. Lemma 12. The modification set M (τ, σ) = {Tτ (x),i ◦ τ : x ∈ H(τ, σ) ∧ i ∈ 1 {τ (x) + j · sgn(σ(x) − τ (x)) : j ∈ k p } ∩ n} is (p + 1)-improving under the raised Minkowski distance Fˆp for p ∈ N \ {0}.

Lemma 3. Both the inequalities |wi,lef t | ≤ 2n − 1 and |wi,right | ≤ 2n − 1 hold. Proof. Let i0 be the start index of wi . Let s0 be a subword incident with Gi , occurring at index i0 . Let i1 be the largest index at which there is an occurrence of a subword left, but not right incident with Gi . Let s1 be this subword. By Lemma 1, s1 is right incident with Gk for some 0 ≤ k < i ≤ p. Suppose i1 ≥ i0 + n. i1 + n), there exists a path from a vertex in V (Gi ) to one in V (Gk ), contradicting Lemma 1.

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