A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
Deterministic coin tossing with applications to optimal parallel list ranking
Information and Control
Combinatorica
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Parallel symmetry-breaking in sparse graphs
SIAM Journal on Discrete Mathematics
Locality in distributed graph algorithms
SIAM Journal on Computing
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
On the complexity of distributed network decomposition
Journal of Algorithms
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Some simple distributed algorithms for sparse networks
Distributed Computing
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the complexity of distributed graph coloring
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Assignment Testers: Towards a Combinatorial Proof of the PCP Theorem
SIAM Journal on Computing
A combinatorial construction of almost-ramanujan graphs using the zig-zag product
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Network decomposition and locality in distributed computation
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Sublogarithmic distributed MIS algorithm for sparse graphs using nash-williams decomposition
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Distributed (δ+1)-coloring in linear (in δ) time
Proceedings of the forty-first annual ACM symposium on Theory of computing
Weak graph colorings: distributed algorithms and applications
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Combinatorial PCPs with Efficient Verifiers
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A new technique for distributed symmetry breaking
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Deterministic distributed vertex coloring in polylogarithmic time
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Distributed coloring in Õ (√log n) Bit Rounds
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
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Numerous problems in Theoretical Computer Science can be solved very efficiently using powerful algebraic constructions. Computing shortest paths, constructing expanders, and proving the PCP Theorem, are just a few examples of this phenomenon. The quest for combinatorial algorithms that do not use heavy algebraic machinery, but have the same (or better) efficiency has become a central field of study in this area. Combinatorial algorithms are often simpler than their algebraic counterparts. Moreover, in many cases, combinatorial algorithms and proofs provide additional understanding of studied problems. In this paper we initiate the study of combinatorial algorithms for Distributed Graph Coloring problems. In a distributed setting a communication network is modeled by a graph G = (V,E) of maximum degree Δ. The vertices of G host the processors, and communication is performed over the edges of G. The goal of distributed vertex coloring is to color V with (Δ+1) colors such that any two neighbors are colored with distinct colors. Currently, efficient algorithms for vertex coloring that require O(Δ + log* n) time are based on the algebraic algorithm of Linial [18] that employs set-systems. The best currently-known combinatorial set-system free algorithm, due to Goldberg, Plotkin, and Shannon [14], requires O(Δ2 + log* n) time. We significantly improve over this by devising a combinatorial (Δ + 1)- coloring algorithm that runs in O(Δ+log* n) time. This exactly matches the running time of the best-known algebraic algorithm. In addition, we devise a tradeoff for computing O(Δ ċ t)-coloring in O(Δ/t + log* n) time, for almost the entire range 1 t O(Δ + log* n) time on general graphs, and in O(log n/ log log n) time on graphs of bounded arboricity. Prior to our work, these results could be only achieved using algebraic techniques. We believe that our algorithms are more suitable for real-life networks with limited resources, such as sensor, ad-hoc, and mobile networks.