Path packing and a related optimization problem
نویسنده
چکیده
Let G = (N, E) be a supply graph, with the node set N and edge set E, and (T, S) be a demand graph, with T ⊆ N , S ∩ E = ∅. Observe paths whose end-vertices form pairs in S (called S-paths). The following path packing problem for graphs is fundamental: what is the maximal number of S-paths in G? In this paper this problem is studied under two assumptions: (a) the node degrees in N \ T are even, and (b) any three distinct pairwise intersecting maximal stable sets A, B, C of (T, S) satisfy A∩B = B ∩C = A∩C (this condition was defined by A. Karzanov in 1989, see [K 1989]). For any demand graph violating (b) the problem is known to be NP-hard even under (a), and only a few cases satisfying (a) and (b) have been solved. In each of the solved cases, a solution and an optimal dual object were defined by a certain auxiliary “weak” multiflow optimization problem whose solutions supply constructive elements for S-paths and concatenate them into an S-path packing by a kind of matching. In this paper the above approach is extended to all demand graphs satisfying (a) and (b), by proving existence of a common solution of the S-path packing and its weak counterpart. The weak problem is very interesting for its own sake, and has connections with such topics as Mader’s edge-disjoint path packing theorem and b-factors in graphs.
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ورودعنوان ژورنال:
- J. Comb. Optim.
دوره 17 شماره
صفحات -
تاریخ انتشار 2009