Listing minimal edge-covers of intersecting families with applications to connectivity problems

Authors:
Zeev Nutov
Affiliations:
The Open University of Israel, 108 Ravutski Street, 43107 Raanana, Israel
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

Let G=(V,E) be a directed/undirected graph, let s,t@?V, and let F be an intersecting family on V (that is, X@?Y,X@?Y@?F for any intersecting X,Y@?F) so that s@?X and t@?X for every X@?F. An edge set I@?E is an edge-cover of F if for every X@?F there is an edge in I from X to V-X. We show that minimal edge-covers of F can be listed with polynomial delay, provided that, for any I@?E the minimal member of the residual family F"I of the sets in F not covered by I can be computed in polynomial time. As an application, we show that minimal undirected Steiner networks, and minimal k-connected and k-outconnected spanning subgraphs of a given directed/undirected graph, can be listed in incremental polynomial time.