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
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
Local Search in Combinatorial Optimization
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On Local Search and Placement of Meters in Networks
SIAM Journal on Computing
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Equivalence of local treewidth and linear local treewidth and its algorithmic applications
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
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)
On the Hardness of Losing Weight
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Searching the k-change neighborhood for TSP is W[1]-hard
Operations Research Letters
Parameterized Complexity
Local search with edge weighting and configuration checking heuristics for minimum vertex cover
Artificial Intelligence
Incremental list coloring of graphs, parameterized by conservation
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Local search: Is brute-force avoidable?
Journal of Computer and System Sciences
The parameterized complexity of local search for TSP, more refined
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Linear-Time computation of a linear problem kernel for dominating set on planar graphs
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
The parameterized complexity of k-flip local search for SAT and MAX SAT
Discrete Optimization
Minimizing rosenthal potential in multicast games
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Parameterized complexity results for exact bayesian network structure learning
Journal of Artificial Intelligence Research
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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 naïve brute-force search of the k-exchange neighborhood requires nO(k) time, which is not practical even for very small values of k. We show that for several classes of sparse graphs, like 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(τ (k) ċ nc), where τ is a function depending on k only and c is a constant independent of k. We demonstrate the applicability of this approach on different problems like 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(2O(k) ċ n2), which is polynomial for k = O(log n). We also complement the algorithms with complexity results indicating that--brute force search is unavoidable--in more general classes of sparse graphs.