Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Simple local search problems that are hard to solve
SIAM Journal on Computing
A survey of approximately optimal solutions to some covering and packing problems
ACM Computing Surveys (CSUR)
Approximating discrete collections via local improvements
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Greedy local improvement and weighted set packing approximation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Approximation algorithms for combinatorial problems
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Approximate local search in combinatorial optimization
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Structure in locally optimal solutions
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
MultiProcessor Scheduling is PLS-Complete
HICSS '09 Proceedings of the 42nd Hawaii International Conference on System Sciences
A survey of approximation results for local search algorithms
Efficient Approximation and Online Algorithms
On the PLS-complexity of maximum constraint assignment
Theoretical Computer Science
| Hi-index | 0.00 |
In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SETCOVER, SETPACKING, and many more. For our investigation, we use the framework of PLS, as defined in Johnson et al., [14]. We show that for most of these problems, computing a locally optimal solution is already PLS-complete for a simple natural neighborhood of size one. For the local search versions of weighted SETPACKING and SETCOVER, we derive tight bounds for a simple neighborhood of size two. To the best of our knowledge, these are one of the very few PLS results about local search for weighted standard set problems.