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 publication constitutes the completely refereed post-workshop lawsuits of the twenty fourth overseas 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 rigorously reviewed and chosen from a complete of ninety one submissions. The papers are prepared in topical sections on algorithms on graphs; algorithms on strings; discrete geometry and satisfiability.

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

Example text

Bn . We call a permutation local if it is an extension of κ. We state the following properties to be met by a metric d in order to be applicable in the forthcoming reduction. Requirement 1 (Optimality of local permutations). Let σ1 , . . , σm ∈ Ext(κ) and k ∈ N. If there is a k-consensus τ ∈ Perm(D) with maxm j=1 d(σj , τ ) ≤ k, then there also is a local permutation τ ∈ Ext(κ) with maxm j=1 d(σj , τ ) ≤ k. In other words, if all voters are local and our metric meets Requirement 1, then we can safely demand that the consensus is local, too, without impairing its chance to satisfy the upper bound k.

Then the Kendall tau distance K is defined by K(σ, τ ) = |K(σ, τ )|. It coincides with the minimum number k of swaps T1 , . . , Tk such that τ = Tk ◦ . . ◦ T1 ◦ σ. If we also allow switching non-adjacent candidates, we obtain the Cayley distance C(σ, τ ), which is the minimum number of transpositions T1 , . . , Tk such that τ = Tk ◦ . . ◦ T1 ◦ σ. A permutation on n can also be specified by its constituent cycles. A cycle C = (x1 x2 . . x|C| ) of ρ ∈ Perm(n) is a (cyclic) sequence of distinct candidates such that ρ(xi ) = xi+1 for 1 ≤ i < |C| and ρ(x|C| ) = x1 .

This view is also taken by the On Maximum Rank Aggregation Problems 17 Hamming distance between strings s, t ∈ {0, 1}n, which is defined as H(s, t) = |{i ∈ n : s(i) = t(i)}| where s(i) denotes the i-th character of s. Let σ, τ ∈ Perm(D). A tuple (x1 , . . , xl ) with xi ∈ D is a common subsequence of σ and τ if i < j ⇔ xi <σ xj ∧ xi <τ xj . Let lcs(σ, τ ) = max{ l : (x1 , . . , xl ) is a common subsequence of σ and τ }. Then the Ulam distance is U (σ, τ ) = n − lcs(σ, τ ). Finally, the Minkowski distance Fp is defined as Fp (σ, τ ) = 1 |σ(x) − τ (x)|p p for p ∈ N \ {0}.

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