Characterization of efficiently parallel solvable problems on distance-hereditary graphs

Sun Yuan Hsieh, Chin Wen Ho, Tsan Sheng Hsu, Ming Tat Ko, Gen Huey Chen

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

In this paper, we sketch common properties of a class of so-called subgraph optimization problems that can be systematically solved on distance-hereditary graphs. Based on the found properties, we then develop a general problem-solving paradigm that solves these problems efficiently in parallel. As a by-product, we also obtain new linear-time algorithms by a sequential simulation of our parallel algorithms. Let Td(|V|, |E|) and Pd(|V|, |E|) denote the time and processor complexities, respectively, required to construct a decomposition tree of a distance-hereditary graph G = (V, E) on a PRAM model Md. Based on the proposed paradigm, we show that the maximum independent set problem, the maximum clique problem, the vertex connectivity problem, the domination problem, and the independent domination problem can be sequentially solved in O(|V| + |E|) time, and solved in parallel in O(Td(|V|, |E|) + log |V|) time using O(Pd(|V|, |E|) + |V|/log |V|) processors on Md. By constructing a decomposition tree under a CREW PRAM, we also show that Td(|V|, |E|) = O(log2 |V|) and Pd(|V|, |E|) = O(|V| + |E|).

Original languageEnglish
Pages (from-to)488-518
Number of pages31
JournalSIAM Journal on Discrete Mathematics
Volume15
Issue number4
DOIs
Publication statusPublished - 2002 Jul

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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