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
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
Arboricity and bipartite subgraph listing algorithms
Information Processing Letters
On the complexity of distributed network decomposition
Journal of Algorithms
Simple distributed&Dgr; + 1-coloring of graphs
Information Processing Letters
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
On the complexity of distributed graph coloring
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Distributive graph algorithms Global solutions from local data
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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
Distributed coloring in Õ (√log n) Bit Rounds
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
A new technique for distributed symmetry breaking
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Deploying wireless networks with beeps
DISC'10 Proceedings of the 24th international conference on Distributed computing
Distributed graph coloring in a few rounds
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Toward more localized local algorithms: removing assumptions concerning global knowledge
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Distributed deterministic edge coloring using bounded neighborhood independence
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Distributed coloring depending on the chromatic number or the neighborhood growth
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Trading bit, message, and time complexity of distributed algorithms
DISC'11 Proceedings of the 25th international conference on Distributed computing
Combinatorial algorithms for distributed graph coloring
DISC'11 Proceedings of the 25th international conference on Distributed computing
Locality and checkability in wait-free computing
DISC'11 Proceedings of the 25th international conference on Distributed computing
Node-Disjoint multipath spanners and their relationship with fault-tolerant spanners
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
On the locality of some NP-complete problems
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Multipath spanners via fault-tolerant spanners
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
Symmetry breaking depending on the chromatic number or the neighborhood growth
Theoretical Computer Science
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Consider an n-vertex graph G = (V,E) of maximum degree Δ, and suppose that each vertex v ∈ V hosts a processor. The processors are allowed to communicate only with their neighbors in G. The communication is synchronous, i.e., it proceeds in discrete rounds. In the distributed vertex coloring problem the objective is to color G with Δ + 1, or slightly more than Δ + 1, colors using as few rounds of communication as possible. (The number of rounds of communication will be henceforth referred to as running time. Efficient randomized algorithms for this problem are known for more than twenty years [1, 19]. Specifically, these algorithms produce a Δ + 1)-coloring within O(log n) time, with high probability. On the other hand, the best known deterministic algorithm that requires polylogarithmic time employs O(Δ2) colors. This algorithm was devised in a seminal FOCS'87 paper by Linial [16]. Its running time is O(log* n). In the same paper Linial asked whether one can color with significantly less than Δ2 colors in deterministic polylogarithmic time. By now this question of Linial became one of the most central long-standing open questions in this area. In this paper we answer this question in the affirmative, and devise a deterministic algorithm that employs Δ1+o(1) colors, and runs in polylogarithmic time. Specifically, the running time of our algorithm is O(f(Δ) log Δ log n, for an arbitrarily slow-growing function f(Δ) = ω(1). We can also produce O(Δ1 + η)-coloring in O(log Δ log n)-time, for an arbitrarily small constant η 0, and O(Δ)-coloring in O(Δε log n) time, for an arbitrarily small constant ε 0. Our results are, in fact, far more general than this. In particular, for a graph of arboricity a, our algorithm produces an O(a1 + η)-coloring, for an arbitrarily small constant η 0, in time O(log a log n).