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58
What Can Be Computed Locally?
 SIAM J. Comput
, 1993
"... . The purpose of this paper is a study of computation that can be done locally in a distributed network, where "locally" means within time (or distance) independent of the size of the network. Locally Checkable Labeling (LCL) problems are considered, where the legality of a labeling can be checked l ..."
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Cited by 112 (1 self)
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. The purpose of this paper is a study of computation that can be done locally in a distributed network, where "locally" means within time (or distance) independent of the size of the network. Locally Checkable Labeling (LCL) problems are considered, where the legality of a labeling can be checked locally (e.g., coloring). The results include the following: ffl There are nontrivial LCL problems that have local algorithms. ffl There is a variant of the dining philosophers problem that can be solved locally. ffl Randomization cannot make an LCL problem local; i.e., if a problem has a local randomized algorithm then it has a local deterministic algorithm. ffl It is undecidable, in general, whether a given LCL has a local algorithm. ffl However, it is decidable whether a given LCL has an algorithm that operates in a given time t. ffl Any LCL problem that has a local algorithm has one that is orderinvariant (the algorithm depends only on the order of the processor id's). Keywords: ...
Network Decomposition and Locality in Distributed Computation (Extended Abstract)
, 1989
"... ) Baruch Awerbuch Department of Mathematics and Laboratory for Computer Science M.I.T. Cambridge, MA 02139 Andrew V. Goldberg y Department of Computer Science Stanford University Stanford, CA 94305 Michael Luby z International Computer Science Institute Berkeley, CA 94704 Serge A. Plo ..."
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Cited by 84 (5 self)
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) Baruch Awerbuch Department of Mathematics and Laboratory for Computer Science M.I.T. Cambridge, MA 02139 Andrew V. Goldberg y Department of Computer Science Stanford University Stanford, CA 94305 Michael Luby z International Computer Science Institute Berkeley, CA 94704 Serge A. Plotkin x Department of Computer Science Stanford University Stanford, CA 94305 May 1989 Abstract We introduce a concept of network decomposition, the essence of which is to partition an arbitrary graph into smalldiameter connected components, such that the graph created by contracting each component into a single node has low chromatic number. We present an efficient distributed algorithm for constructing such a decomposition, and demonstrate its use for design of efficient distributed algorithms. Our method yields new deterministic distributed algorithms for finding a maximal independent set and for (\Delta + 1)coloring of graphs with maximum degree \Delta. These algorithms run...
The String Edit Distance Matching Problems with Moves
, 2006
"... The edit distance between two strings S and R is defined to be the minimum number of character inserts, deletes and changes needed to convert R to S. Given a text string t of length n, and a pattern string p of length m, informally, the string edit distance matching problem is to compute the smalles ..."
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Cited by 58 (3 self)
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The edit distance between two strings S and R is defined to be the minimum number of character inserts, deletes and changes needed to convert R to S. Given a text string t of length n, and a pattern string p of length m, informally, the string edit distance matching problem is to compute the smallest edit distance between p and substrings of t. We relax the problem so that (a) we allow an additional operation, namely, substring moves, and (b) we allow approximation of this string edit distance. Our result is a near linear time deterministic algorithm to produce a factor of O(log n log ∗ n) approximation to the string edit distance with moves. This is the first known significantly subquadratic algorithm for a string edit distance problem in which the distance involves nontrivial alignments. Our results are obtained by embedding strings into L1 vector space using a simplified parsing technique we call Edit
Greed is Good: Approximating Independent Sets in Sparse and . . .
, 1994
"... ... for short, is one of the ~implest, most efficient, and most thoroughly studied methods for finding independent sets in graphs. We show that it surprisingly achieves a performance ratio of (A+ 2)/3 for approximating independent sets in graphs with degree bounded by A. The analysis directs us tow ..."
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Cited by 56 (7 self)
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... for short, is one of the ~implest, most efficient, and most thoroughly studied methods for finding independent sets in graphs. We show that it surprisingly achieves a performance ratio of (A+ 2)/3 for approximating independent sets in graphs with degree bounded by A. The analysis directs us towards a simple parallel and distributed algorithm with identical performance, which on constantdegree graphs runs in O(log ” n) time using linear number of processors. We also analyze the Greedy algorithm when run in combination with a fractional relaxation technique of Nemhauser and Trotter, and obtain an improved (2Z + 3)/5 performance ratio on graphs with average degree ~. Finally, we introduce a generally applicable technique for improving the approximation ratios of independent set algorithms, and illustrate it by improving the performance ratio of Greedy for large ∆.
A LogStar Distributed Maximal Independent Set Algorithm . . .
 PODC'08
, 2008
"... We present a novel distributed algorithm for the maximal independent set (MIS) problem. On growthbounded graphs (GBG) our deterministic algorithm finishes in O(log ∗ n) time, n being the number of nodes. In light of Linial’s Ω(log ∗ n) lower bound our algorithm is asymptotically optimal. Our algori ..."
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Cited by 48 (15 self)
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We present a novel distributed algorithm for the maximal independent set (MIS) problem. On growthbounded graphs (GBG) our deterministic algorithm finishes in O(log ∗ n) time, n being the number of nodes. In light of Linial’s Ω(log ∗ n) lower bound our algorithm is asymptotically optimal. Our algorithm answers prominent open problems in the ad hoc/sensor network domain. For instance, it solves the connected dominating set problem for unit disk graphs in O(log ∗ n) time, exponentially faster than the stateoftheart algorithm. With a new extension our algorithm also computes a δ + 1 coloring in O(log ∗ n) time, where δ is the maximum degree of the graph.
Fast Deterministic Distributed Maximal Independent Set Computation on GrowthBounded Graphs
 IN PROC. 19TH CONFERENCE ON DISTRIBUTED COMPUTING (DISC
, 2005
"... The distributed complexity of computing a maximal independent set in a graph is of both practical and theoretical importance. While there exists an elegant O(log n) time randomized algorithm for general graphs [20], no deterministic polylogarithmic algorithm is known. In this paper, we study the p ..."
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Cited by 40 (12 self)
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The distributed complexity of computing a maximal independent set in a graph is of both practical and theoretical importance. While there exists an elegant O(log n) time randomized algorithm for general graphs [20], no deterministic polylogarithmic algorithm is known. In this paper, we study the problem in graphs with bounded growth, an important family of graphs which includes the wellknown unit disk graph and many variants thereof. Particularly, we propose a deterministic algorithm that computes a maximal independent set in time O(log \Delta * log*n) in graphs with bounded growth, where n and \Delta denote the number of nodes and the maximal degree in G, respectively.
Coloring unstructured radio networks
, 2005
"... During and immediately after their deployment, ad hoc and sensor networks lack an efficient communication scheme rendering even the most basic network coordination problems difficult. Before any reasonable communication can take place, nodes must come up with an initial structure that can serve as ..."
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Cited by 36 (9 self)
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During and immediately after their deployment, ad hoc and sensor networks lack an efficient communication scheme rendering even the most basic network coordination problems difficult. Before any reasonable communication can take place, nodes must come up with an initial structure that can serve as a foundation for more sophisticated algorithms. In this paper, we consider the problem of obtaining a vertex coloring as such an initial structure. We propose an algorithm that works in the unstructured radio network model. This model captures the characteristics of newly deployed ad hoc and sensor networks, i.e. asynchronous wakeup, no collisiondetection, and scarce knowledge about the network topology. When modeling the network as a graph with bounded independence, our algorithm produces a correct coloring with O(∆) colors in time O( ∆ log n) with high probability, where n and ∆ are the number of nodes in the network and the maximum degree, respectively. Also, the number of locally used colors depends only on the local node density. Graphs with bounded independence generalize unit disk graphs as well as many other wellknown models for
A New Parallel Algorithm For The Maximal Independent Set Problem
, 1989
"... A new parallel algorithm for the maximal independent set problem is constructed. It runs in O(log 4 n) time when implemented on a linear number of EREWprocessors. This is the first deterministic algorithm for the maximal independent set problem (MIS) whose running time is polylogarithmic and whose ..."
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Cited by 35 (2 self)
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A new parallel algorithm for the maximal independent set problem is constructed. It runs in O(log 4 n) time when implemented on a linear number of EREWprocessors. This is the first deterministic algorithm for the maximal independent set problem (MIS) whose running time is polylogarithmic and whose processortime product is optimal up to a polylogarithmic factor.
Parallel Algorithms with Optimal Speedup for Bounded Treewidth
 Proceedings 22nd International Colloquium on Automata, Languages and Programming
, 1995
"... We describe the first parallel algorithm with optimal speedup for constructing minimumwidth tree decompositions of graphs of bounded treewidth. On nvertex input graphs, the algorithm works in O((logn)^2) time using O(n) operations on the EREW PRAM. We also give faster parallel algorithms with opti ..."
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Cited by 33 (10 self)
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We describe the first parallel algorithm with optimal speedup for constructing minimumwidth tree decompositions of graphs of bounded treewidth. On nvertex input graphs, the algorithm works in O((logn)^2) time using O(n) operations on the EREW PRAM. We also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth, including all decision problems expressible in monadic secondorder logic. On nvertex input graphs, the algorithms use O(n) operations together with O(log n log n) time on the EREW PRAM, or O(log n) time on the CRCW PRAM.