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Computer Science > Discrete Mathematics

arXiv:1408.3977 (cs)
[Submitted on 18 Aug 2014]

Title:Spanning Tree Enumeration in 2-trees: Sequential and Parallel Perspective

Authors:Vandhana.C, S.Hima Bindhu, P.Renjith, N.Sadagopan, B.Supraja
View a PDF of the paper titled Spanning Tree Enumeration in 2-trees: Sequential and Parallel Perspective, by Vandhana.C and S.Hima Bindhu and P.Renjith and N.Sadagopan and B.Supraja
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Abstract:For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components. A vertex separator $S$ is minimal if it contains no other separator as a strict subset and a minimum vertex separator is a minimal vertex separator of least cardinality. A {\em clique} is a set of mutually adjacent vertices. A 2-tree is a connected graph in which every maximal clique is of size three and every minimal vertex separator is of size two. A spanning tree of a graph $G$ is a connected and an acyclic subgraph of $G$. In this paper, we focus our attention on two enumeration problems, both from sequential and parallel perspective. In particular, we consider listing all possible spanning trees of a 2-tree and listing all perfect elimination orderings of a chordal graph. As far as enumeration of spanning trees is concerned, our approach is incremental in nature and towards this end, we work with the construction order of the 2-tree, i.e. enumeration of $n$-vertex trees are from $n-1$ vertex trees, $n \geq 4$. Further, we also present a parallel algorithm for spanning tree enumeration using $O(2^n)$ processors. To our knowledge, this paper makes the first attempt in designing a parallel algorithm for this problem. We conclude this paper by presenting a sequential and parallel algorithm for enumerating all Perfect Elimination Orderings of a chordal graph.
Comments: 9 pages, 2 figures
Subjects: Discrete Mathematics (cs.DM); Data Structures and Algorithms (cs.DS)
Cite as: arXiv:1408.3977 [cs.DM]
  (or arXiv:1408.3977v1 [cs.DM] for this version)
  https://doi.org/10.48550/arXiv.1408.3977
arXiv-issued DOI via DataCite

Submission history

From: Sadagopan Narasimhan [view email]
[v1] Mon, 18 Aug 2014 11:19:02 UTC (46 KB)
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