Topic
P-complete
About: P-complete is a research topic. Over the lifetime, 22 publications have been published within this topic receiving 2142 citations.
Papers
TL;DR: For P- complete problems such as traveling salesperson, cycle covers, 0-1 integer programming, multicommodity network flows, quadratic assignment, etc., it is shown that the approximation problem is also P-complete.
Abstract: For P-complete problems such as traveling salesperson, cycle covers, 0-1 integer programming, multicommodity network flows, quadratic assignment, etc., it is shown that the approximation problem is also P-complete. In contrast with these results, a linear time approximation algorithm for the clustering problem is presented.
1,878 citations
TL;DR: It is shown that the problem of computing source-sink reliability is NP-hard, in fact P-complete, even for undirected and acyclic directed source-Sink planar graphs having vertex degree at most three.
Abstract: We show that the problem of computing source-sink reliability is NP-hard, in fact # P-complete, even for undirected and acyclic directed source-sink planar graphs having vertex degree at most three. Thus the source-sink reliability problem is unlikely to have an efficient algorithm, even when the graph can be laid out on a rectilinear grid.
112 citations
14 Oct 1974
TL;DR: The class of P-Complete problems is studied and it is shown that for any constant e ≫0 there is a P-complete problem for which an e-approximate solution can be found in linear time.
Abstract: We study the class of P-Complete problems and show the following: i) for any constant e ≫0 there is a P-complete problem for which an e-approximate solution can be found in linear time ii) there exist P-Complete problems for which linear time approximate solutions that get closer and closer to the optimal (with increasing problem size) can be found iii) there exist P-Complete problems for which the approximation problems are also P-Complete
45 citations
TL;DR: It is shown that the Ziv-Lempel algorithm and two standard variations are P-complete, Hence an efficient parallelization of these algorithms is not possible unless P = NC.
39 citations
17 Sep 1997
TL;DR: It is shown that this problem is Σ2P complete and some related results on the complexity of ILP are derived and the usefulness of such complexity results are discussed.
Abstract: The bounded ILP-consistency problem for function-free Horn clauses is described as follows. Given a set E+ and E− of function-free ground Horn clauses and an integer k polynomial in E+∪E−, does there exist a function-free Horn clause C with no more than k literais such that C subsumes each element in E+ and C does not subsume any element in E−. It is shown that this problem is Σ 2 P complete. We derive some related results on the complexity of ILP and discuss the usefulness of such complexity results.
31 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2015 | 1 |
| 2006 | 1 |
| 2005 | 1 |
| 2001 | 2 |
| 2000 | 1 |
| 1998 | 1 |