K. Cattell, M. Dinneen, and M. Fellows. Obstructions to within a few vertices or edges of acyclic, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of members of the obstruction sets is used to guarantee that termination of the algorithm will result. Cattell, Dinneen, Downey, Fellows, and Langston were successful in using this method to determine members of the obstruction set for graphs with feedback vertex sets and feedback edge sets 2 [5]. Building upon their idea of computing obstructions, we too have implemented a way to compute the planar members of O fi 4 . 18 Chapter 4 Reductions Let G be a class of graphs. A reduction R is a finite set (R; Gamma R ) where R i is a acceptable graph and Gamma R i is the resulting ....

K. Cattell, M. Dinneen, and M. Fellows. Obstructions to within a few vertices or edges of acyclic, 1995.

.... of order at least 3w 3 for pathwidth w) Some general methods for computing the obstructions to a given family of graphs have also been proposed [14, 20] These methods are nontrivial since their use requires a tree decomposition of bounded width and additional problem specific information [11]. Hence, their application has been limited [10, 11] In this paper we define a new metric # of a graph and show that it is a lower bound for the treewidth of the graph. In practice, this bound can be computed in time linear in the size of the graph. Besides being of independent interest, our ....

.... Some general methods for computing the obstructions to a given family of graphs have also been proposed [14, 20] These methods are nontrivial since their use requires a tree decomposition of bounded width and additional problem specific information [11] Hence, their application has been limited [10, 11]. In this paper we define a new metric # of a graph and show that it is a lower bound for the treewidth of the graph. In practice, this bound can be computed in time linear in the size of the graph. Besides being of independent interest, our bound gives a new perspective on the obstructions for ....

K. Cattell, M. J. Dinneen, and M. R. Fellows, Obstructions to within a few vertices or edges of acyclic, in Proc. Workshop on Algorithms and Data Structures, Kingston, Ontario, Canada, 1995, Lecture Notes in Comput. Sci., 955 (1995), pp. 415--427.

....of tokens in practice. Since the pebbling proceeds according to a greedy strategy with much flexibility, there may be placement heuristics that can improve its performance on typical instances. For applications in the theory of graph minors (in particular, in the theory of obstruction sets [9, 10, 11, 13]) it would be interesting to know whether an analog of Theorem 1 can be proved for treewidth. For these applications the proof need not be given, as it is here, in the form of an efficient algorithm a purely structural argument would suffice. ....

K. Cattell, M. J. Dinneen, and M. R. Fellows. Obstructions to within a few vertices or edges of acyclic. In Proceedings of the Fourth Workshop on Algorithms and Data Structures, WADS'95, in Lecture Notes in Computer Science. Springer-Verlag, August 1995.

.... This approach was first successfully used to find the obstructions for the graph families with small vertex covers, k Vertex Cover, 1 i 5 (see [3] This current paper is a full version, including new results, of our workshop paper on computing several feedback vertex and edge set obstructions [4]. Graphs with small feedback sets are desirable for many reasons. One specific application deals with the task of minimizing costs in the construction of broadcastdisplay networks. For this particular model we have two types of nodes and two types of connecting lines. Each node can display and ....

....since any disconnected obstruction O of the lower ideal k Feedback Vertex Set is a union of graphs from 28 Table 2 Summary of our 2 Feedback Vertex Set obstruction set computation. Pathwidth Four Prefixes Boundaried Minimal Total for Feedback Vertex Set 2 Obstructions t parses proofs [0,1,2,3,4,01,02,0,03,12] 0 [0,1,2,3,4,01,02,0,01,13] 0 [0,1,2,3,4,01,02,03,0,12] 0 [0,1,2,3,4,01,02,03,12,14] 0 [0,1,2,3,4,01,02,03,14,24] 0 [0,1,2,3,4,01,02,03,12,13] 0 [0,1,2,3,4,01,02,03,04,12] 1 15 211 [0,1,2,3,4,01,02,03,0,04] 0 [0,1,2,3,4,01,02,0,01,12] 0 150 2251 [0,1,2,3,4,01,02,0,03,04] 0 233 3271 ....

[Article contains additional citation context not shown here]

Kevin Cattell, Michael J. Dinneen, and Michael R. Fellows. Obstructions to within a few vertices or edges of acyclic. In Proceedings of the Fourth Workshop on Algorithms and Data Structures, WADS'95, volume 955 of Lecture Notes on Computer Science, pages 415--427. Springer-Verlag, August 1995.

....F equals fG j (G) kg for some integer constant k. Several studied graph families such as k Vertex Cover (graphs with a vertex cover of cardinality at most k) and k Feedback Vertex Set are typical examples, for which a few of these families have recently been characterized by obstructions [CD94, CDF95]. Given a minor order lower ideal F , often (but not always) another class fk F j k 0g of parameterized and finitely characterizable graph families is obtained by defining lower ideals that are within k vertices (or edges) of F . That is, for a fixed family F , the following parameterized ....

Kevin Cattell, Michael J. Dinneen, and Michael R. Fellows. Obstructions to within a few vertices or edges of acyclic. In Proceedings of the Fourth Workshop on Algorithms and Data Structures, WADS'95, volume 955 of Lecture Notes on Computer Science, pages 415--427. Springer-Verlag, August 1995.

....O of F obstructions. iii) A decision algorithm for a finite index congruence for F . Then O can be effectively computed. Perhaps surprisingly, the algorithm of [FL89b] has been implemented and nontrivial, previously unknown obstruction sets for interesting ideals 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, ....

K. Cattell, M. J. Dinneen and M. R. Fellows. Obstructions to within a few vertices or edges of acyclic. Proc. Workshop on Algorithms and Data Structures, Springer-Verlag, Lecture Notes in Computer Science vol. 955 (1995), 415--427.

....if we are given the information: v) An MSO expression OE that describes the graphs of the lower ideal F . Then from this we can effectively derive (i) iii) and (iv) This result is mainly due to Courcelle [Co90] 5) Other work on the systematic computation of obstruction sets has appeared in [Pr93, APS90, CD94, CDF95, Kin94, KL91]. Some of these results support practical implementations that have led to some significant mechanical or partly mechanical proofs of new and nontrivial forbidden substructure theorems. There has been a considerable amount of overlapping work in this area which is sometimes confusing to sort ....

.... that the algorithm of Theorem A terminates can be replaced by an explicit calculation of a stopping time computable from the index of the congruence [Lag93] Perhaps surprisingly, Theorem A can be implemented and a number of previously unknown obstruction sets have been mechanically computed [CD94, CDF95]. The Holy Grail of such efforts would be a computation of the obstruction set for torus embedding, which probably contains about 2,000 graphs. Theorem A can also be adapted to other partial orders, including those such as the topological order, that are not a wqo. It can be shown in this case ....

[Article contains additional citation context not shown here]

K. Cattell, M. J. Dinneen and M. R. Fellows. Obstructions to within a few vertices or edges of acyclic. Proceedings WADS'95, Springer-Verlag, Lecture Notes in Computer Science vol. 955 (1995), 415--427.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC