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Showing 1 to 8 of 8 for “"maximum cardinality"”.
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A Sparsification Based Algorithm for Maximum-Cardinality Bipartite Matching in Planar Graphs
… the one of special interest to us being the Maximum Cardinality Bipartite Matching in Planar Graphs. In this work, we present a novel sparsification based approach for computing maximum/perfect bipartite matching in planar graphs. The overall complexity of our algorithm is O(n<sup>6/5</sup> …
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A Separator-Based Framework for Graph Matching Problems
… particular interest is the problem of finding a maximum cardinality matching of a graph. Also of interest is the weighted variant: the problem of computing a minimum-cost maximum cardinality matching. For an arbitrary graph with m edges and n vertices, there are known, long-standing combinatorial …
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Matchings, matroids and submodular functions
… we give an algorithm for constructing perfect or maximum cardinality matchings in non-bipartite graphs. Our algorithm requires O(n") time in graphs with n vertices, where w < 2.38 is the matrix multiplication exponent. This algorithm achieves the best-known running time for dense graphs, and it …
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Combinatorics of finite sets
… then among the intersecting subfamilies of I of maximum cardinality there is a star. In Chapter 1, we prove Chvatal's conjecture for several special cases. Let I be an ideal in 2$\sp{\lbrack n\rbrack }$ that is compressed with respect to a given element. We prove that among the largest …
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Alliance Partitions in Graphs.
… alliance partition number</em>) is the maximum cardinality of a partition of <em>V</em> into defensive alliances (respectively, strong defensive alliances). The <em>global (strong) alliance partition number</em> is defined similarly. For each parameter we give both general bounds and …
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Combinatorial incremental problems
… problems, including e/2e-1approximation for the maximum weight matching problem, and a e/e+1 approximation for submodular valuations. In Chapter 4 we introduce a discrete-concavity property that allows us to give constant approximation guarantees to several problems, including an asymptotic …
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Bounds on the cardinalities of nearly neighborly and neighborly families of polytopes
… quadrilaterals and conjecture that this is the maximum. Using techniques developed by J. Zaks for nearly-neighborly tetrahedra, we show that a family of nearly neighborly quadrilaterals has at most 14 members. A family of nearly neighborly quadrilaterals is said to share a base line if all …
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Algorithms and hardness results for the jump number problem, the joint replenishment problem, and the optimal clustering of frequency-constrained maintenance jobs
… jump number of a 2D2C poset is equivalent to the maximum cardinality of an independent set in a properly defined collection of rectangles in the plane. We then model the geometric problem as a linear program. Even though the underlying polytope may not be integral, we show that one can always find …