Online computation and competitive analysis
Online computation and competitive analysis
Balls and bins: a study in negative dependence
Random Structures & Algorithms
SIAM Journal on Computing
How asymmetry helps load balancing
Journal of the ACM (JACM)
Balanced Allocations: The Heavily Loaded Case
SIAM Journal on Computing
Balanced allocations: the weighted case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
Constant-Time Approximation Algorithms via Local Improvements
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
An improved constant-time approximation algorithm for maximum~matchings
Proceedings of the forty-first annual ACM symposium on Theory of computing
An algorithmic approach to the lovász local lemma. I
Random Structures & Algorithms
Space-efficient local computation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Distance approximation in bounded-degree and general sparse graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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We propose a general method for converting online algorithms to local computation algorithms, by selecting a random permutation of the input, and simulating running the online algorithm. We bound the number of steps of the algorithm using a query tree, which models the dependencies between queries. We improve previous analyses of query trees on graphs of bounded degree, and extend this improved analysis to the cases where the degrees are distributed binomially, and to a special case of bipartite graphs. Using this method, we give a local computation algorithm for maximal matching in graphs of bounded degree, which runs in time and space O(log3n). We also show how to convert a large family of load balancing algorithms (related to balls and bins problems) to local computation algorithms. This gives several local load balancing algorithms which achieve the same approximation ratios as the online algorithms, but run in O(logn) time and space. Finally, we modify existing local computation algorithms for hypergraph 2-coloring and k-CNF and use our improved analysis to obtain better time and space bounds, of O(log4n), removing the dependency on the maximal degree of the graph from the exponent.