Combinatorial network abstraction by trees and distances
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation(2008)
摘要
We draw attention to combinatorial network abstraction problems. These are specified by a class P of pattern graphs and a real-valued similarity measure @r that is based on certain graph properties. For a fixed pattern P and similarity measure @r, the optimization task on a given graph G is to find a subgraph G^'@?G which belongs to P and minimizes @r(G,G^'). In this work, we consider this problem for the natural and somewhat general case of trees and distance-based similarity measures. In particular, we systematically study spanning trees of graphs that minimize distances, approximate distances, and approximate closeness-centrality with respect to standard vector- and matrix-norms. Complexity analysis within a unifying framework shows that all considered variants of the problem are NP-complete, except for the case of distance-minimization with respect to the norm L"~. If a subset of edges can be ''forced'' into the spanning tree, no polynomial-time constant-factor approximation algorithmexists for the distance-approximation problems unless P=NP.
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关键词
real-valued similarity measure,approximate distance,distance-approximation problem,matrix norms,approximate closeness-centrality,network abstraction,np-completeness,distance-based similarity measure,inapproximability,class p,graph g,spanning trees,similarity measure,subgraph g,certain graph property,combinatorial network abstraction,polynomial time,spanning tree
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