Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Note on the convergence of simulated annealing algorithms
SIAM Journal on Control and Optimization
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
A constant factor approximation algorithm for a class of classification problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
On Local Search and Placement of Meters in Networks
SIAM Journal on Computing
Parameterized complexity of finding subgraphs with hereditary properties
Theoretical Computer Science
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Algorithm Design
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Polynomial Time Approximation Schemes for MAX-BISECTION on Planar and Geometric Graphs
SIAM Journal on Computing
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Theoretical Aspects of Local Search (Monographs in Theoretical Computer Science. An EATCS Series)
Theoretical Aspects of Local Search (Monographs in Theoretical Computer Science. An EATCS Series)
Improved Approximation Algorithms for Minimum Weight Vertex Separators
SIAM Journal on Computing
On the Hardness of Losing Weight
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Improved upper bounds for vertex cover
Theoretical Computer Science
Searching the k-change neighborhood for TSP is W[1]-hard
Operations Research Letters
The parameterized complexity of k-flip local search for SAT and MAX SAT
Discrete Optimization
On the hardness of losing weight
ACM Transactions on Algorithms (TALG)
Incremental list coloring of graphs, parameterized by conservation
Theoretical Computer Science
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Many local search algorithms are based on searching in the k-exchange neighborhood. This is the set of solutions that can be obtained from the current solution by exchanging at most k elements. As a rule of thumb, the larger k is, the better are the chances of finding an improved solution. However, for inputs of size n, a naive brute-force search of the k-exchange neighborhood requires n^O^(^k^) time, which is not practical even for very small values of k. We show that for several classes of sparse graphs, including planar graphs, graphs of bounded vertex degree and graphs excluding some fixed graph as a minor, an improved solution in the k-exchange neighborhood for many problems can be found much more efficiently. Our algorithms run in time O(@t(k)@?n^c), where @t is a function depending only on k and c is a constant independent of k and n. We demonstrate the applicability of this approach on a variety of problems including r-Center, Vertex Cover, Odd Cycle Transversal, Max-Cut, and Min-Bisection. In particular, on planar graphs, all our algorithms searching for a k-local improvement run in time O(2^O^(^k^)@?n^2), which is polynomial for k=O(logn). We complement these fixed-parameter tractable algorithms for k-local search with parameterized intractability results indicating that brute-force search is unavoidable in more general classes of graphs.