By Julio Araujo, Jean-Claude Bermond, Frédéric Giroire (auth.), Costas S. Iliopoulos, William F. Smyth (eds.)
This booklet constitutes the completely referred post-workshop lawsuits of the twenty second overseas Workshop on Combinatorial Algorithms, IWOCA 2011, held in Vancouver, BC, Canada, in July 2011.
The 30 revised complete papers provided have been conscientiously reviewed and chosen from a complete of seventy one submissions. A vast number of issues in combinatorics and graph concept are addressed, corresponding to combinatorics on phrases, string algorithms, codes, Venn diagrams, set walls; Hamiltonian & Eulerian homes, graph drawing, colouring, dominating units, spanning bushes, and others.
Read Online or Download Combinatorial Algorithms: 22nd International Workshop, IWOCA 2011, Victoria, BC, Canada, July 20-22, 2011, Revised Selected Papers PDF
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Additional resources for Combinatorial Algorithms: 22nd International Workshop, IWOCA 2011, Victoria, BC, Canada, July 20-22, 2011, Revised Selected Papers
Example text
As we show below, however, the problem is FPT in two important classes of graphs, namely apex-minorfree graphs (which include planar graphs as a special case) and chordal graphs. Recall that it is NP-complete to decide if a planar graph admits a proper 3coloring [18]. As a consequence, the Graph Coloring problem parameterized by the number of colors is not even in XP in planar graphs. Our result for planar graphs thus brings out a marked difference in the parameterized complexity of these two problems when restricted to planar graphs.
Later, we show that the same pLPF algorithm can be used to construct the LCP array and the LP F array for traditional strings. Crochemore and Ilie [1] identify that the traditional LP F array is a permutation of the well-studied LCP array. We observe the same relationship in terms of the pLP F and pLCP arrays. 40 R. Beal and D. Adjeroh Proposition 2. The pLP F array is a permutation of pLCP . This observation allows us to view the pLCP array from a different perspective. As a novel use of our compute pLPF algorithm, we introduce a way to construct the pLCP array in linear time.
We also make all vertices in K pairwise adjacent and all vertices in I pairwise independent. This completes the construction. Suppose φ admits a satisfying truth assignment χ. Let D = {v[x] ∈ K : χ(x) = 1}. We now prove that this choice of D is a split dominating set. Consider u[C] ∈ I. There exists at least one x ∈ V such that x ∈ ν(C) and χ(x) = 1. Thus the corresponding vertex v[x] ∈ D, and u[C] is dominated. Further, consider the all-negative clause Cˆ corresponding to C, that contains every variable in V that is not in ν(C).