K. Cattell, M. J. Dinneen, R. G. Downey, M. R. Fellows, and M. A. Langston. On computing graph minor obstruction sets. Theor. Comp. Sc., 233:107--127, 2000. Home/Search Document Details and Download
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On Characterizing Graphs With Branchwidth At Most Four - Riggins (Correct)
.... because without the bounded treewidth property, we can only construct the MSOL formula once already having established the obstruction set [7] Bodlaender and Thilikos proved the existence of a sentence in monadic secondorder logic formula expressing whether a graph has branchwidth at most k [4]. Even though the result and proof are non constructive, at least we know that one exists. Research done in the past to compute obstruction sets by MSOL grammar was not computationally a good idea. With the increase of supercomputing resources and the advances in parallel computing, the idea of ....
K. Cattell, M. Dinneen, R. Downey, M. Fellows, and M. Langston. On computing graph minor obstruction sets. The Journal of Universal Computer Science, 1995.
Parameterized Complexity for the Skeptic - Downey (2003) (15 citations) Self-citation (Downey) (Correct)
....set in general. But again this situation is akin to that of regular languages where the data is presented in such a way to be useful. Some progress has been done towards 11 understanding what information is needed for such effective generation of the obstruction sets. See, for example, [CDDFL00, CDF97]. 5 Connections with Classical Complexity 5.1 PTAS s In the first section, we were introduced to some rather impractical PTAS s. They were from STOC, SODA etc. They are in fact only a small sample of such. Here area couple of others. The PTAS for the UNBOUNDED BATCH SCHEDULING problem due to ....
K. Cattell, M. Dinneen, R. Downey, M. Fellows, and M. Langston, "On Computing Graph Minor Obstruction Sets," Theor. Comp. Science. Vol. 233 (2000), 107-127.
Parameterized Complexity After (Almost) 10 Years: Review and.. - Downey, Fellows Self-citation (Downey Fellows) (Correct)
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K. Cattell, M. Dinneen, R. Downey and M. Fellows, "On Computing Graph Minor Obstruction Sets," Theoretical Computer Science A, to appear.
Parameterized Complexity: A Framework for Systematically.. - Downey, Fellows, Stege (1997) (41 citations) Self-citation (Downey Fellows) (Correct)
....Claim 1. that has finite index, and Claim 2. that D D implies D F D , where F = F k . This allows us to conclude that F k has finite index on t boundaried digraphs. Our definition of is based on a set of abstract tests in the sense of the method of test sets developed and exposited in [FL89, AF93, CDDFL98, DF98]. A test T is specified by the following information: 1. A partition of f1; tg into two subsets, the red subset TR and the blue subset TB . 2. A boundary starter set S f1; tg. We will use k 0 to denote the size of S. 3. A positive integer k 1 such that k 0 k 1 k. We will use k ....
K. Cattell, M. Dinneen, R. Downey and M. Fellows, "On Computing Graph Minor Obstruction Sets," Theoretical Computer Science A, to appear.
A Note on the Computability of Graph Minor Obstruction.. - Courcelle, Downey.. (1997) Self-citation (Downey Fellows) (Correct)
....in this general area. For example, it is unknown whether the obstruction set for an arbitrary union of ideals F = F 1 [ F 2 can be computed from the two corresponding obstruction sets O 1 and O 2 , although this can be accomplished if at least one of these obstruction sets includes a tree [CDDFL97]. The main theorem of this paper significantly extends the negative result of [FL89a] We prove the following for the minor ordering. Theorem 1. There is no effective procedure to compute the obstruction set for a minor ideal F from a monadic second order (MSO) description of F . This should be ....
.... have been successfully computed [CD94, CDF95] Since (i) and (iii) can be effectively derived from an MSO description of F [Co90a] our Theorem 1 shows that (ii) is essential in the earlier positive result of [FL89b] Other work on the systematic computation of obstruction sets has appeared in [APS90, CDDFL97, GI91, Kin94, KL91, LA91, Lag93, Pr93]. 2 Preliminaries All of our discussion concerns finite simple graphs. A graph H is a minor of a graph G if a graph isomorphic to H can be obtained from G by a sequence of operations chosen from the list: i) delete a vertex, ii) delete an edge, iii) contract an edge. When applying the edge ....
K. Cattell, M. J. Dinneen, R. G. Downey, M. R. Fellows and M. A. Langston. On computing graph minor obstruction sets. Manuscript available from mfellows@csr.uvic.ca, 1997.
Thomas Wolle - Arie Koster Hans (2004) (Correct)
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K. Cattell, M. J. Dinneen, R. G. Downey, M. R. Fellows, and M. A. Langston. On computing graph minor obstruction sets. Theor. Comp. Sc., 233:107--127, 2000.
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