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Distributed computing with advice: Information sensitivity of graph coloring
 IN 34TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP
, 2007
"... We study the problem of the amount of information (advice) about a graph that must be given to its nodes in order to achieve fast distributed computations. The required size of the advice enables to measure the information sensitivity of a network problem. A problem is information sensitive if litt ..."
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Cited by 22 (10 self)
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We study the problem of the amount of information (advice) about a graph that must be given to its nodes in order to achieve fast distributed computations. The required size of the advice enables to measure the information sensitivity of a network problem. A problem is information sensitive if little advice is enough to solve the problem rapidly (i.e., much faster than in the absence of any advice), whereas it is information insensitive if it requires giving a lot of information to the nodes in order to ensure fast computation of the solution. In this paper, we study the information sensitivity of distributed graph coloring.
Local Management of a Global Resource in a Communication Network
 PROC. OF IEEE FOCS
, 1987
"... This paper introduces a new distributed data object called Resource Controller which provides an abstraction for managing the consumption of a global resource in a distributed system. Examples of resources that may be managed by such an object include; number of messages sent, number of nodes par ..."
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Cited by 19 (5 self)
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This paper introduces a new distributed data object called Resource Controller which provides an abstraction for managing the consumption of a global resource in a distributed system. Examples of resources that may be managed by such an object include; number of messages sent, number of nodes participating in the protocol, and total CPU time consumed. The Resource Controller object is accessed through a procedure that can be invoked at any node in the network. Before consuming a unit of resource at some node, the controlled algorithm should invoke the procedure at this node, requesting a permit to consume a unit of the resource. The procedure returns either a permit or a rejection. The key characteristics of the Resource Controller object are the constraints that it imposes on the global resource consumption. An (M; W)Controller guarantees that the total number of permits granted is at most M ; it also ensures that if a request is rejected then at least M \Gamma W permits a...
A New Technique For Distributed Symmetry Breaking
 In Symp. on Principles of Distributed Computing
, 2010
"... We introduce MultiTrials, a new technique for symmetry breaking for distributed algorithms and apply it to various problems in general graphs. For instance, we present three randomized algorithms for distributed (vertex or edge) coloring improving on previous algorithms and showing a time/color tra ..."
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Cited by 19 (6 self)
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We introduce MultiTrials, a new technique for symmetry breaking for distributed algorithms and apply it to various problems in general graphs. For instance, we present three randomized algorithms for distributed (vertex or edge) coloring improving on previous algorithms and showing a time/color tradeoff. To get a ∆ + 1 coloring takes time O(log ∆ + √ log n). To obtain an O( ∆ + log 1+1 / log ∗ n n) coloring takes time O(log ∗ n). This is more than an exponential improvement in time for graphs of polylogarithmic degree. Our fastest algorithm works in constant time using O( ∆ log (c) n + log 1+1/c n) colors, where c denotes an arbitrary constant and log (c) n denotes the c times (recursively) applied logarithm to n. We also use the MultiTrials technique to compute network decompositions and to compute maximal independent set (MIS), obtaining new results for several graph classes.
Connected Components in O(log 3/2 n) Parallel Time for the CREW PRAM
"... Finding the connected components of an undirected graph G = (V; E) on n = jV j vertices and m = jEj edges is a fundamental computational problem. The best known parallel algorithm for the CREW PRAM model runs in O(log 2 n) time using n 2 = log 2 n processors [6, 15]. For the CRCW PRAM model, ..."
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Cited by 15 (2 self)
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Finding the connected components of an undirected graph G = (V; E) on n = jV j vertices and m = jEj edges is a fundamental computational problem. The best known parallel algorithm for the CREW PRAM model runs in O(log 2 n) time using n 2 = log 2 n processors [6, 15]. For the CRCW PRAM model, in which concurrent writing is permitted, the best known algorithm runs in O(log n) time using slightly more than (n +m)= log n processors [26, 9, 5]. Simulating this algorithm on the weaker CREW model increases its running time to O(log 2 n) [10, 19, 29]. We present here a simple algorithm that runs in O(log 3=2 n) time using n +m CREW processors. Finding an o(log 2 n) parallel connectivity algorithm for this model was an open problem for many years. 1 Introduction Let G = (V; E) be an undirected graph on n = jV j vertices and m = jEj edges. A path p of length k is a sequence of edges (e 1 ; \Delta \Delta \Delta ; e i ; \Delta \Delta \Delta ; e k ) such that e i 2 E for i = 1; \...
Maintaining Dynamic Sequences under Equality Tests In Polyiogarithmic Time
, 1997
"... We present a randomized and a deterministic data structure for maintaining a dynamic family of sequences under equality tests of pairs of sequences and creations of new sequences by joining or splitting existing sequences. Both data structures support equality tests in O ( 1) time. The randomized v ..."
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Cited by 15 (0 self)
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We present a randomized and a deterministic data structure for maintaining a dynamic family of sequences under equality tests of pairs of sequences and creations of new sequences by joining or splitting existing sequences. Both data structures support equality tests in O ( 1) time. The randomized version supports new sequence creations in O(log 2 n) expected time where n is the length of the sequence created. The deterministic solution supports sequence creations in O (log n (log m log * m +log n)) time for the mth operation.
Sublogarithmic Distributed MIS Algorithm for Sparse Graphs using NashWilliams Decomposition
 In Journal of Distributed Computing Special Issue of selected papers from PODC
, 2008
"... We study the distributed maximal independent set (henceforth, MIS) problem on sparse graphs. Currently, there are known algorithms with a sublogarithmic running time for this problem on oriented trees and graphs of bounded degrees. We devise the first sublogarithmic algorithm for computing MIS on gr ..."
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Cited by 15 (2 self)
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We study the distributed maximal independent set (henceforth, MIS) problem on sparse graphs. Currently, there are known algorithms with a sublogarithmic running time for this problem on oriented trees and graphs of bounded degrees. We devise the first sublogarithmic algorithm for computing MIS on graphs of bounded arboricity. This is a large family of graphs that includes graphs of bounded degree, planar graphs, graphs of bounded genus, graphs of bounded treewidth, graphs that exclude a fixed minor, and many other graphs. We also devise efficient algorithms for coloring graphs from these families. These results are achieved by the following technique that may be of independent interest. Our algorithm starts with computing a certain graphtheoretic structure, called NashWilliams forestsdecomposition. Then this structure is used to compute the MIS or coloring. Our results demonstrate that this methodology is very powerful. Finally, we show nearlytight lower bounds on the running time of any distributed algorithm for computing a forestsdecomposition.
Structural Parallel Algorithmics
, 1991
"... The first half of the paper is a general introduction which emphasizes the central role that the PRAM model of parallel computation plays in algorithmic studies for parallel computers. Some of the collective knowledgebase on nonnumerical parallel algorithms can be characterized in a structural way ..."
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Cited by 11 (4 self)
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The first half of the paper is a general introduction which emphasizes the central role that the PRAM model of parallel computation plays in algorithmic studies for parallel computers. Some of the collective knowledgebase on nonnumerical parallel algorithms can be characterized in a structural way. Each structure relates a few problems and technique to one another from the basic to the more involved. The second half of the paper provides a bird'seye view of such structures for: (1) list, tree and graph parallel algorithms; (2) very fast deterministic parallel algorithms; and (3) very fast randomized parallel algorithms. 1 Introduction Parallelism is a concern that is missing from "traditional" algorithmic design. Unfortunately, it turns out that most efficient serial algorithms become rather inefficient parallel algorithms. The experience is that the design of parallel algorithms requires new paradigms and techniques, offering an exciting intellectual challenge. We note that it had...
A Distributed Algorithm to Find kdominating Sets
, 1999
"... We consider a connected undirected graph G(n; m) with n nodes and m edges. A kdominating set D in G is a set of nodes having the property that every node in G is at most k edges away from at least one node in D. ..."
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Cited by 11 (0 self)
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We consider a connected undirected graph G(n; m) with n nodes and m edges. A kdominating set D in G is a set of nodes having the property that every node in G is at most k edges away from at least one node in D.
Efficient computation of implicit representations of sparse graphs
 Discrete Applied Mathematics
, 1997
"... The problem of finding an implicit representation for a graph such that vertex adjacency can be tested quickly is fundamental to all graph algorithms. In particular, it is possible to represent sparse graphs on n vertices using O(n) space such that vertex adjacency is tested in O(1) time. We show he ..."
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Cited by 10 (0 self)
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The problem of finding an implicit representation for a graph such that vertex adjacency can be tested quickly is fundamental to all graph algorithms. In particular, it is possible to represent sparse graphs on n vertices using O(n) space such that vertex adjacency is tested in O(1) time. We show here how to construct such a representation efficiently by providing simple and optimal algorithms, both in a sequential and a parallel setting. Our sequential algorithm runs in O(n) time. The parallel algorithm runs in O(log n) time using O(n=log n) CRCW PRAM processors, or in O(log n log n) time using O(n = log n log
Distributed (∆ + 1)coloring in linear (in ∆) time
 In Proc. 41st Annual ACM Symposium on Theory of Computing (STOC
, 2009
"... The distributed ( ∆ + 1)coloring problem is one of most fundamental and wellstudied problems in Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms published. The current stateoftheart running time is O( ∆ log ∆+log ∗ ..."
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Cited by 10 (0 self)
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The distributed ( ∆ + 1)coloring problem is one of most fundamental and wellstudied problems in Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms published. The current stateoftheart running time is O( ∆ log ∆+log ∗ n), due to Kuhn and Wattenhofer, PODC’06. Linial (FOCS’87) has proved a lower bound of 1 2 log ∗ n for the problem, and Szegedy and Vishwanathan (STOC’93) provided a heuristic argument that shows that algorithms from a wide family of locally iterative algorithms are unlikely to achieve running time smaller than Θ( ∆ log ∆). We present a deterministic (∆+1)coloring distributed algorithm with running time O(∆)+ 1