T. V. Wimer, S. T. Hedetniemi, and R. Laskar. A methodology for constructing linear graph algorithms. Congressus Numerantium, 50:43--60, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....results were obtained along these lines. Eventually, a theory was developed, that explained the linearity of the previously published algorithms, predicted the existence of several thousand new linear time algorithms of this kind and provided a methodology for constructing any one of them [24]. The problem addressed in this paper is that of finding the cardinality of a minimum vertex cover, in the particular case of a two terminal series parallel graph. Furthermore, we define the problem in a real time environment and compare the performance of a parallel algorithm to that of a ....

....accuracy of the solutions computed in both cases. We begin by describing some previous results that will help us build our parallel algorithm for solving the above stated problem. This is followed by an outline of the results obtained in this paper. 1. 1 Previous work The framework elaborated in [24] can be applied to any family of graphs which can be defined recursively by certain rules of composition involving finite sets of terminals. The construction process of a member of such a recursive family of graphs can be modeled as a tree. The leaves of the tree represent base graphs of the ....

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T.V. Wimer, S.T. Hedetniemi and R. Laskar, "A methodology for constructing linear graph algorithms", Congressus Numerantium 50 (1985), pp. 43-60. 18

.... that fixing a natural parameter k implies that the yes instances have bounded treewidth or pathwidth (for examples see [5, 15, 18] We also know that many problems can be solved in linear time when the input includes a bounded width path decomposition (or tree decomposition) of the graph (see [1, 2, 4, 12, 25] and [6] for many further references) After several rounds of improvement [23, 17, 19] the best known algorithm for finding tree decompositions is due to Bodlaender [7] For each fixed k, this algorithm in time O(2 k 2 n) either determines that the treewidth is greater than k, or produces a ....

T. V. Wimer, S. T. Hedetniemi and R. Laskar. A methodology for constructing linear graph algorithms. Congressus Numerantium 50 (1985), 43--60. 11

....tree T . In the general case, however, the decision problem for n p (G) is NP complete, even when restricted to bipartite or chordal graphs. For the first result, a dynamic programming style algorithm is constructed using a blend of methodologies developed by Wimer in 1988 [10] as illustrated in [11] and [7] and by Mitchell in 1977 [9] as illustrated in [3] The class of (rooted) trees can be constructed recursively from copies of a single vertex, K 1 , using only one rule of composition. This rule combines two rooted trees (T 1 ; r 1 ) and (T 2 ; r 2 ) by adding an edge between r 1 and r 2 ....

T.V. Wimer, S.T. Hedetniemi, and R. Laskar. A methodology for constructing linear graph algorithms. Congr. Numer. 50(1985), 43-60.

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T. V. Wimer, S. T. Hedetniemi, and R. Laskar. A methodology for constructing linear graph algorithms. Congressus Numerantium, 50:43--60, 1985.

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T. V. WIMER, S. T. HEDETNIEMI, AND R. LASKAR, A methodology for constructing linear graph algorithms, DCS, Clemson University, September 1985.

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