Abstract | ||
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In this paper, we partially address a question raised by David Karger [5] regarding the structure of maximum-weighted bipartite matchings when the affinity data is of low rank. The affinity data of a weighted bipartite graph G over the vertex sets U = V = {1,.,n} means the n×n matrix W whose entry W ij is the weight of the edge (i,j) of G, 1 ≤ i,j ≤ n. W has rank at most r if there are 2r vector u 1,.,u r, v 1,.v r â̂̂ ân such that In particular, we study the following locality property of the matchings: For an integer k > 0, we say the locality of G is at most k if for every matching π of G, either π has the maximum weight, or its weight is smaller than that of another matching σ with |π â̂-σ| ≤ k and |σ â̂-π| ≤ k. We prove the following theorem: For every W â̂̂ [0,1]n×n of rank r and ε â̂̂ [0,1], there exists such that (i) has rank at most r + 1, (ii) and (iii) the weighted bipartite graph with affinity data has locality at most âŒ̂r/ε⌉ r . © 2013 Springer-Verlag Berlin Heidelberg. |
Year | DOI | Venue |
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2013 | 10.1007/978-3-642-38768-5_63 | COCOON |
Field | DocType | Volume |
Rank (linear algebra),Discrete mathematics,Combinatorics,Perturbation theory,Vertex (geometry),Matrix (mathematics),Bipartite graph,Rank (graph theory),Matching (graph theory),Mean reciprocal rank,Mathematics | Conference | 7936 LNCS |
Issue | ISSN | Citations |
null | 16113349 | 0 |
PageRank | References | Authors |
0.34 | 5 | 2 |
Name | Order | Citations | PageRank |
---|---|---|---|
Xingwu Liu | 1 | 19 | 12.77 |
Shang-Hua Teng | 2 | 3927 | 424.26 |