Locality in distributed graph algorithms
SIAM Journal on Computing
Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q
Journal of Combinatorial Theory Series B
SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Large deviations for sums of partly dependent random variables
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
Fast Distributed Approximations in Planar Graphs
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Leveraging Linial's Locality Limit
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Constant-Time Approximation Algorithms via Local Improvements
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds for local approximation
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
ACM Computing Surveys (CSUR)
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König's theorem states that on bipartite graphs the size of a maximum matching equals the size of a minimum vertex cover. It is known from prior work that for every ε0 there exists a constant-time distributed algorithm that finds a (1+ε)-approximation of a maximum matching on 2-coloured graphs of bounded degree. In this work, we show--somewhat surprisingly--that no sublogarithmic-time approximation scheme exists for the dual problem: there is a constant δ0 so that no randomised distributed algorithm with running time o(logn) can find a (1+δ)-approximation of a minimum vertex cover on 2-coloured graphs of maximum degree 3. In fact, a simple application of the Linial---Saks (1993) decomposition demonstrates that this lower bound is tight. Our lower-bound construction is simple and, to some extent, independent of previous techniques. Along the way we prove that a certain cut minimisation problem, which might be of independent interest, is hard to approximate locally on expander graphs.