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72
What Cannot Be Computed Locally!
 In Proceedings of the 23 rd ACM Symposium on the Principles of Distributed Computing (PODC
, 2004
"... We give time lower bounds for the distributed approximation of minimum vertex cover (MVC) and related problems such as minimum dominating set (MDS). In k communication rounds, MVC and MDS can only be approximated by factors# /k) and # /k) for some constant c, where n and # denote the number ..."
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Cited by 141 (28 self)
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We give time lower bounds for the distributed approximation of minimum vertex cover (MVC) and related problems such as minimum dominating set (MDS). In k communication rounds, MVC and MDS can only be approximated by factors# /k) and # /k) for some constant c, where n and # denote the number of nodes and the largest degree in the graph. The number of rounds required in order to achieve a constant or even only a polylogarithmic approximation ratio is at log n/ log log n) and#1 #/ log log #). By a simple reduction, the latter lower bounds also hold for the construction of maximal matchings and maximal independent sets.
A Functional Approach to External Graph Algorithms
 Algorithmica
, 1998
"... . We present a new approach for designing external graph algorithms and use it to design simple external algorithms for computing connected components, minimum spanning trees, bottleneck minimum spanning trees, and maximal matchings in undirected graphs and multigraphs. Our I/O bounds compete w ..."
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Cited by 108 (2 self)
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. We present a new approach for designing external graph algorithms and use it to design simple external algorithms for computing connected components, minimum spanning trees, bottleneck minimum spanning trees, and maximal matchings in undirected graphs and multigraphs. Our I/O bounds compete with those of previous approaches. Unlike previous approaches, ours is purely functionalwithout side effectsand is thus amenable to standard checkpointing and programming language optimization techniques. This is an important practical consideration for applications that may take hours to run. 1 Introduction We present a divideandconquer approach for designing external graph algorithms, i.e., algorithms on graphs that are too large to fit in main memory. Our approach is simple to describe and implement: it builds a succession of graph transformations that reduce to sorting, selection, and a recursive bucketing technique. No sophisticated data structures are needed. We apply our t...
The price of being nearsighted
 In SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
, 2006
"... Achieving a global goal based on local information is challenging, especially in complex and largescale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible tradeoff between the amount of local information and the quality o ..."
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Cited by 86 (12 self)
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Achieving a global goal based on local information is challenging, especially in complex and largescale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible tradeoff between the amount of local information and the quality of the global solution for general covering and packing problems. Specifically, we give a distributed algorithm using only small messages which obtains an (ρ∆) 1/kapproximation for general covering and packing problems in time O(k 2), where ρ depends on the LP’s coefficients. If message size is unbounded, we present a second algorithm that achieves an O(n 1/k) approximation in O(k) rounds. Finally, we prove that these algorithms are close to optimal by giving a lower bound on the approximability of packing problems given that each node has to base its decision on information from its kneighborhood. 1
Lowcomplexity distributed scheduling algorithms for wireless networks
 IEEE/ACM Trans. on Netw
"... Abstract — We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. ..."
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Cited by 84 (9 self)
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Abstract — We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. The first algorithm requires each link to collect local queuelength information in its neighborhood, and its complexity is independent of the size and topology of the network. The second algorithm is presented for the nodeexclusive interference model, does not require nodes to collect queuelength information even in their local neighborhoods, and its complexity depends only on the maximum node degree in the network. I.
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 76 (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.
Removing Randomness in Parallel Computation Without a Processor Penalty
 Journal of Computer and System Sciences
, 1988
"... We develop some general techniques for converting randomized parallel algorithms into deterministic parallel algorithms without a blowup in the number of processors. One of the requirements for the application of these techniques is that the analysis of the randomized algorithm uses only pairwise in ..."
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Cited by 61 (1 self)
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We develop some general techniques for converting randomized parallel algorithms into deterministic parallel algorithms without a blowup in the number of processors. One of the requirements for the application of these techniques is that the analysis of the randomized algorithm uses only pairwise independence. Our main new result is a parallel algorithm for coloring the vertices of an undirected graph using at most \Delta + 1 distinct colors in such a way that no two adjacent vertices receive the same color, where \Delta is the maximum degree of any vertex in the graph. The running time of the algorithm is O(log 3 n log log n) using a linear number of processors on a concurrent read, exclusive write (CREW) parallel random access machine (PRAM). 1 Our techniques also apply to several other problems, including the maximal independent set problem and the maximal matching problem. The application of the general technique to these last two problems is mostly of academic interest because...
Fast Deterministic Distributed Maximal Independent Set Computation on GrowthBounded Graphs
 In Proc. of the 19th International Symposium on Distributed Computing (DISC
, 2005
"... Abstract. 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 st ..."
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Cited by 47 (10 self)
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Abstract. 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 ∆ · log∗n) in graphs with bounded growth, where n and ∆ denote the number of nodes and the maximal degree in G, respectively. 1
Distributed weighted matching
 Lecture Notes in Computer Science
"... In this paper, we present fast distributed approximation algorithms for matching in weighted trees and general weighted graphs. The time complexity as well as the approximation ratio of the tree algorithm is constant. For the general graph algorithm we prove a constant ratio bound and a polylogarit ..."
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Cited by 44 (2 self)
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In this paper, we present fast distributed approximation algorithms for matching in weighted trees and general weighted graphs. The time complexity as well as the approximation ratio of the tree algorithm is constant. For the general graph algorithm we prove a constant ratio bound and a polylogarithmic time complexity of O(log2 n).
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 42 (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 Algorithmic Techniques for Combinatorial Computation
 Ann. Rev. Comput. Sci
, 1988
"... this paper and supplied many helpful comments. This research was supported in part by NSF grants DCR8511713, CCR8605353, and CCR8814977, and by DARPA contract N0003984C0165. ..."
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Cited by 35 (3 self)
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this paper and supplied many helpful comments. This research was supported in part by NSF grants DCR8511713, CCR8605353, and CCR8814977, and by DARPA contract N0003984C0165.