Efficient algorithms for finding minimum spanning forests of hierarchically defined graphs

doi:10.1016/0196-6774(87)90042-3

Journal of Algorithms

Volume 8, Issue 2, June 1987, Pages 260-284

https://doi.org/10.1016/0196-6774(87)90042-3 Get rights and content

Abstract

In an earlier paper (T. Lengauer, Efficient solution of connectivity problems on hierarchically defined graphs, in Reihe “Theoretische Informatik” No. 24, FB 17, Universität-Gesamthochschule Paderborn, Paderborn, West Germany, 1985. (Excerpts in “Proceedings of the WG '85” (H. Noltemeier, Ed.) Trauner Verlag, Linz, Austria, 1985)) a hierarchical graph model is defined that allows the exploitation of the hierarchy for the more efficient solution of graph problems on very large graphs. The model is motivated by applications in the design of VLSI circuits. We show how to efficiently find minimum spanning forests in this graph model. We solve decision problems pertaining to minimum spanning forests in almost linear time in the length of the hierarchical description, query problems in time linear in the depth of the hierarchy and we construct minimum spanning forests in space linear in the length of the hierarchical description.

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^☆: A preliminary version of this paper is published in the “Proceedings of STACS 86” (B. Monien and G. Vidal-Naquet, Eds.), Lecture Notes in Computer Science Vol. 210, pp. 153–170, Springer-Verlag, Berlin/New York/Heidelberg, 1986.

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Efficient algorithms for finding minimum spanning forests of hierarchically defined graphs☆

Abstract

Computers and Intractibility: A Guide to the Theory of NP-Completeness

The HILL-System: A design environment for the hierarchical specification, compaction, and simulation of integrated circuit layouts

Fast algorithms for findings nearest common ancestors

The complexity of compacting hierarchically specified layouts of integrated circuits