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Hector R. Wong,Thomas P. Shanley them if either their intervals intersect or they belong to the same row. We show that recognition of the class of strip graphs is .-complete even if all intervals are of length 2. Strip graphs are important to the study of job selection, where we need an equivalence relation to connect multiple int

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https://doi.org/10.1007/978-1-4899-2218-2r of used ADMs. We first present efficient approximation algorithms with approximation factor of 2 ln (. . .) + .(ln (. . .)) for any fixed node degree bound . and grooming factor ., and 2ln .+ .( ln .) in unbounded degree directed trees, respectively. In the attempt of extending our results to gene

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https://doi.org/10.1007/978-1-4757-2778-4bility vectors to detect the communities, see Latapy and Pons [2005]. In this paper we focus on the first part of such an approach . the computation of the probability vectors for the random walks, and propose a more efficient algorithm for computing these vectors in time complexity that is linear i

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Michel Chrétien,Kenneth W. McKernsal comparability graphs are comparability graphs of posets of dimension four. Among other uses, this gives an implicit representation of a chordal comparability graph using .(.) integers so that, given two vertices, it can be determined in .(1) time whether they are adjacent, no matter how dense the

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Molecular Biology of Chromosome Functionobes such that . can be embedded into a graph of . by adding edges between certain nonprobes. If the partition of the vertices is a part of the input we call . a partitioned probe graph of .. In this paper we show that there exists a polynomial-time algorithm for the recognition of partitioned probe

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https://doi.org/10.1007/978-1-4612-0241-7polynomial and the two-variable interlace polynomial of a graph . of clique-width at most . with . vertices can be computed in time .(. .), where .(.) ≤3 for the inerlace polynomial, .(.) ≤2.+1 for the matching polynomial and .(.) ≤3 .2. for the chromatic polynomial.

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Molecular Biology of Drug Addictionsubgraphs of .-trees. n this paper, we investigate the family of edge-maximal graphs of branchwidth ., that we call .-branches. The .-branches are, just as the .-trees, a subclass of the chordal graphs where all minimal separators have size .. However, a striking difference arises when considering s

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https://doi.org/10.1007/978-1-4020-8243-6mially solvable, contrasting its APX-hardness for the case of unlimited availability of items. However, if the underlying graph is a grid, and edge multiplicities are one, we show that it is even NP-complete to approximate the maximum profit to within a factor . ..

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