NDLI: Path packing and a related optimization problem

Content Provider	Springer Nature Link
Author	Vanetik, Natalia
Copyright Year	2007
Abstract	Let G 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 Linear Algebra Appl. 114–115:293–328, 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.
Starting Page	192
Ending Page	205
Page Count	14
File Format	PDF
ISSN	13826905
Journal	Journal of Combinatorial Optimization
Volume Number	17
Issue Number	2
e-ISSN	15732886
Language	English
Publisher	Springer US
Publisher Date	2007-11-02
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Path packing Multiflow K-clutter Operations Research/Decision Theory Optimization Theory of Computation Mathematical Modeling and Industrial Mathematics Convex and Discrete Geometry Combinatorics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Discrete Mathematics and Combinatorics Computational Theory and Mathematics Computer Science Applications

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