NDLI: Optimal Reduction of Two-Terminal Directed Acyclic Graphs

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kamburowski, Jerzy Stallmann, Matthias F. M. Bein, Wolfgang W.
Copyright Year	1992
Abstract	Algorithms for series-parallel graphs can be extended to arbitrary two-terminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit in-degree (out-degree) into its sole incoming (outgoing) neighbor. This paper gives an $O(n^{2.5} )$ algorithm for minimizing node reductions, based on vertex cover in a transitive auxiliary graph. Applications include the analysis of PERT networks, dynamic programming approaches to network problems, and network reliability. For NP-hard problems one can obtain algorithms that are exponential only in the minimum number of node reductions rather than the number of vertices. This gives improvements if the underlying graph is nearly series-parallel.
Starting Page	1112
Ending Page	1129
Page Count	18
File Format	PDF
ISSN	00975397
DOI	10.1137/0221065
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6
Volume Number	21
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	transitive graph algorithms complexity Reliability, availability, maintenance, inspection reliability Structural characterization of families of graphs directed acyclic graph dynamic programming series-parallel graph Graph theory PERT network Programming involving graphs or networks Analysis of algorithms and problem complexity triconnected components NP-completeness Directed graphs (digraphs), tournaments Graph algorithms Dynamic programming Reliability, testing and fault tolerance
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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