کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
430752 | 688140 | 2008 | 13 صفحه PDF | دانلود رایگان |

This paper investigates a graph enumeration problem, called the maximal P-subgraphs problem, where P is a hereditary or connected-hereditary graph property. Formally, given a graph G, the maximal P-subgraphs problem is to generate all maximal induced subgraphs of G that satisfy P. This problem differs from the well-known node-deletion problem, studied by Yannakakis and Lewis [J. Lewis, On the complexity of the maximum subgraph problem, in: Proc. 10th Annual ACM Symposium on Theory of Computing, ACM Press, New York, USA, 1978, pp. 265–274; M. Yannakakis, Node- and edge-deletion NP-complete problems, in: Proc. 10th Annual ACM Symposium on Theory of Computing, ACM Press, New York, USA, 1978, pp. 253–264; J. Lewis, M. Yannakakis, The node-deletion problem for hereditary properties is NP-complete, J. Comput. System Sci. 20 (2) (1980) 219–230]. In the maximal P-subgraphs problem, the goal is to produce all (locally) maximal subgraphs of a graph that have property P, whereas in the node-deletion problem, the goal is to find a single (globally) maximum size subgraph with property P. Algorithms are presented that reduce the maximal P-subgraphs problem to an input-restricted version of this problem. These algorithms imply that when attempting to efficiently solve the maximal P-subgraphs problem for a specific P, it is sufficient to solve the restricted case. The main contributions of this paper are characterizations of when the maximal P-subgraphs problem is in a complexity class C (e.g., polynomial delay, total polynomial time).
Journal: Journal of Computer and System Sciences - Volume 74, Issue 7, November 2008, Pages 1147-1159