Abstract
This paper deals with the root choice strategy for a tree decomposition when multiple agents(processors) are deployed. Tree decomposition is one of the most important decompositions in graph theory. It not only plays a role in theoretical investigations but also has widely practical applications [4]. The first step of solving problem using tree decomposition is to choose a root. And the root choice affects the time complexity when parallel processing is employed. We propose an algorithm to determine the root which makes the latest completion time minimum. In addition, remarks and future works are given.
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References
Arnborg, S.: Efficient algorithms for combinatorial problems on graphs with bounded decomposability - A survey. BIT 25, 2–23 (1985)
Arnborg, S., Lagergren, J.: Easy problems for tree-decomposable graphs. Journal of Algorithms 12, 308–349 (1991)
Arnborg, S., Proskurowski, A.: Linear time algorithms for NP-hard problems restricted to partial k-trees. Disc. Appl. Math. 23, 11–24 (1989)
Bodlaender, H.L.: Treewidth: Characterizations, Applications, and Computations. In: Fomin, F.V. (ed.) WG 2006. LNCS, vol. 4271, pp. 1–14. Springer, Heidelberg (2006)
Borie, R.B.: Recursively Constructed Graph Families. PhD thesis, School of Information and Computer Science, Georgia Institute of Technology (1988)
Borie, R.B., Parker, R.G., Tovey, C.A.: Automatic generation of lineartime algorithms from predicate calculus descriptions of problems on recursively constructed graph families. Algorithmica 7, 555–581 (1992)
Hu, T.C.: Parallel sequencing and assembly line problems. Operations Research 9, 841–848 (1961)
Lauritzen, S.J., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. The Journal of the Royal Statistical Society Series B (Methodological) 50, 157–224 (1988)
Robertson, N., Seymour, P.D.: Graph minors (II) Algorithmic aspects of tree-width. J. Algorithms 7, 309–322 (1986)
Thorup, M.: Structured programs have small tree-width and good register allocation. Information and Computation 142, 159–181 (1998)
Wimer, T.V.: Linear Algorithms on k-Terminal Graphs. PhD thesis, Dept. of Computer Science, Clemson University (1987)
Wimer, T.V., Hedetniemi, S.T., Laskar, R.: A methodology for constructing linear graph algorithms. Congressus Numerantium 50, 43–60 (1985)
Wu, T.H.: Fiber network service survivability. Artech House, Inc., Norwood (1992)
Yamaguchi, A., Aoki, K.F., Mamitsuka, H.: Graph complexity of chemical compounds in biological pathways. Genome Informatics 14, 376–377 (2003)
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Li, Y., Lu, Y. (2008). A Note on Root Choice for Parallel Processing of Tree Decompositions. In: Nguyen, N.T., Jo, G.S., Howlett, R.J., Jain, L.C. (eds) Agent and Multi-Agent Systems: Technologies and Applications. KES-AMSTA 2008. Lecture Notes in Computer Science(), vol 4953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78582-8_72
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DOI: https://doi.org/10.1007/978-3-540-78582-8_72
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78581-1
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