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- W24716939 abstract "We consider a framework for bi-objective network construction problems where one objective is to be maximized while the other is to be minimized. Given a host graph G = (V, E) with edge weights we ∈ Z and edge lengths le ∈ N for e ∈ E we define the density of a pattern subgraph H = (V′, E′) ⊆ G as the ratio ∂(H) =Σe∈E′ we/Σe∈E′ le We consider the problem of computing a maximum density pattern H with weight at least W and and length at most L in a host G.We consider this problem for different classes of hosts and patterns. We show that it is NP-hard even if the host has treewidth 2 and the pattern is a path. However, it can be solved in pseudo-polynomial linear time if the host has bounded treewidth and the pattern is a graph from a given minor-closed family of graphs. Finally, we present an FPTAS for a relaxation of the density maximization problem, in which we are allowed to violate the upper bound on the length at the cost of some penalty." @default.
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- W24716939 date "2011-01-01" @default.
- W24716939 modified "2023-09-23" @default.
- W24716939 title "The Density Maximization Problem in Graphs" @default.
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- W24716939 doi "https://doi.org/10.1007/978-3-642-22685-4_3" @default.
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