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- W2014313757 abstract "We consider the problem of finding a strictly fundamental cycle basis of minimum weight in the cycle space associated with an undirected connected graph G , where a nonnegative weight is assigned to each edge of G and the total weight of a basis is defined as the sum of the weights of all the cycles in the basis. Several heuristics have been proposed to tackle this NP -hard problem, which has some interesting applications. In this paper we show that this problem is APX -hard, even when restricted to unweighted graphs, and hence does not admit a polynomial-time approximation scheme, unless P = NP . Using a recent result on the approximability of lower-stretch spanning trees (Elkin et al. (2005) [7] ), we obtain that the problem is approximable within O ( log 2 n log log n ) for arbitrary graphs. We obtain tighter approximability bounds for dense graphs. In particular, the problem restricted to complete graphs admits a polynomial-time approximation scheme." @default.
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- W2014313757 date "2011-02-01" @default.
- W2014313757 modified "2023-09-29" @default.
- W2014313757 title "On the approximability of the minimum strictly fundamental cycle basis problem" @default.
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- W2014313757 doi "https://doi.org/10.1016/j.dam.2010.10.014" @default.
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