Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
On finding and verifying locally optimal solutions
SIAM Journal on Computing
Simple local search problems that are hard to solve
SIAM Journal on Computing
The complexity of the Lin-Kernighan heuristic for the traveling salesman problem
SIAM Journal on Computing
A note on the complexity of local search problems
Information Processing Letters
Local search, reducibility and approximability of NP-optimization problems
Information Processing Letters
Handbook of combinatorics (vol. 2)
On Local Search for Weighted K-Set Packing
Mathematics of Operations Research
On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
An oracle-polynomial time augmentation algorithm for integer programming
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
New Results on the Old k-opt Algorithm for the Traveling Salesman Problem
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Complexity of Generic Primal Algorithms for Solving General Integer Programs
Mathematics of Operations Research
On the Hardness of Global and Local Approximation
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
0/1-Integer Programming: Optimization and Augmentation are Equivalent
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
A survey of very large-scale neighborhood search techniques
Discrete Applied Mathematics
Approximate Local Search in Combinatorial Optimization
SIAM Journal on Computing
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On the Road to $\mathcal{PLS}$-Completeness: 8 Agents in a Singleton Congestion Game
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
On the complexity of local search for weighted standard set problems
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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
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Local search algorithms for combinatorial optimization problems are in general of pseudopolynomial running time and polynomial-time algorithms are often not known for finding locally optimal solutions for NP-hard optimization problems. We introduce the concept of ε-local optimality and show that an ε-local optimum can be identified in time polynomial in the problem size and 1=ε whenever the corresponding neighborhood can be searched in polynomial time, for ε 0. If the neighborhood can be searched in polynomial time for a δ-local optimum, a variation of our main algorithm produces a (δ + ε)-local optimum in time polynomial in the problem size and 1/ε. As a consequence, a combinatorial optimization problem has a fully polynomial-time approximation scheme if and only if the problem of determining a better solution---the so-called augmentation problem---has a fully polynomial-time approximation scheme.