Locality in distributed graph algorithms
SIAM Journal on Computing
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Applying randomized edge coloring algorithms to distributed communication: an experimental study
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
On the complexity of distributed network decomposition
Journal of Algorithms
Randomized Distributed Edge Coloring via an Extension of the Chernoff--Hoeffding Bounds
SIAM Journal on Computing
Nearly optimal distributed edge coloring in O(log log n) rounds
Random Structures & Algorithms
Near-optimal, distributed edge colouring via the nibble method
ESA '95 Selected papers from the third European symposium on Algorithms
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Distributed O(Delta log(n))-Edge-Coloring Algorithm
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Some simple distributed algorithms for sparse networks
Distributed Computing
On the locality of bounded growth
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
On the complexity of distributed graph coloring
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
A randomized distributed algorithm for the maximal independent set problem in growth-bounded graphs
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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
A log-star distributed maximal independent set algorithm for growth-bounded graphs
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Distributed (δ+1)-coloring in linear (in δ) time
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Weak graph colorings: distributed algorithms and applications
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
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
Toward more localized local algorithms: removing assumptions concerning global knowledge
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
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We study the edge-coloring problem in the message-passing model of distributed computing. This is one of the most fundamental problems in this area. Currently, the best-known deterministic algorithms for (2Δ-1)-edge-coloring requires O(Δ) + log* n time [23], where Δ is the maximum degree of the input graph. Also, recent results of [5] for vertex-coloring imply that one can get an O(Δ)-edge-coloring in O(Δµ" log n) time, and an O(Δ1 + µ)-edge-coloring in O(log Δ log n) time, for an arbitrarily small constant µ 0. In this paper we devise a significantly faster deterministic edge-coloring algorithm. Specifically, our algorithm computes an O(Δ)-edge-coloring in O(Δµ) + log* n time, and an O(Δ1 + µ)-edge-coloring in O(log Δ) + log* n time. This result improves the state-of-the-art running time for deterministic edge-coloring with this number of colors in almost the entire range of maximum degree Δ. Moreover, it improves it exponentially in a wide range of Δ, specifically, for 2©(log* n) ≤ Δ ≤ polylog(n). In addition, for small values of Δ (up to log1 - ? n, for some fixed Δ 0) our deterministic algorithm outperforms all the existing randomized algorithms for this problem. On our way to these results we study the vertex-coloring problem on graphs with bounded neighborhood independence. This is a large family of graphs, which strictly includes line graphs of r-hypergraphs (i.e., hypergraphs in which each hyperedge contains r or less vertices) for r = O(1), and graphs of bounded growth. We devise a very fast deterministic algorithm for vertex-coloring graphs with bounded neighborhood independence. This algorithm directly gives rise to our edge-coloring algorithms, which apply to general graphs. Our main technical contribution is a subroutine that computes an O(Δ/p)-defective p-vertex coloring of graphs with bounded neighborhood independence in O(p2) + log* n time, for a parameter p, 1 d p d Δ. In all previous efficient distributed routines for m-defective p-coloring the product m Å p is super-linear in Δ. In our routine this product is linear in Δ, and this enables us to speed up the coloring drastically.