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93
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 106 (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.
On Chromatic Sums and Distributed Resource Allocation
"... This paper studies an optimization problem that arises in the context of distributed resource allocation: Given a conflict graph that represents the competition of processors over resources, we seek an allocation under which no two jobs with conflicting requirements are executed simultaneously. Our ..."
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Cited by 66 (14 self)
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This paper studies an optimization problem that arises in the context of distributed resource allocation: Given a conflict graph that represents the competition of processors over resources, we seek an allocation under which no two jobs with conflicting requirements are executed simultaneously. Our objective is to minimize the average response time of the system. In alternative formulation this is known as the Minimum Color Sum (MCS) problem [24]. We show, that the algorithm based on finding iteratively a maximum independent set (MaxIS) is a 4approximation to the MCS. This bound is tight to within a factor of 2. We give improved ratios for the classes of bipartite, boundeddegree, and line graphs. The bound generalizes to a 4aeapproximation of MCS for classes of graphs for which the maximum independent set problem can be approximated within a factor of ae. On the other hand, we show that an n1 \Gamma fflapproximation is NPhard, for some ffl? 0. For some instances of the resource allocation problem, such as the Dining Philosophers, an efficient solution requires edge coloring of the conflict graph. We introduce the Minimum Edge Color Sum (MECS) problem which is shown to be NPhard. We show that a 2approximation to MECS(G) can be obtained distributively using compact coloring within O(log² n) communication rounds.
Faultlocal distributed mending
 In Proceedings of the 14th Annual ACM Symposium on Principles of Distributed Computing
, 1995
"... As communication networks grow, existing fault handling tools that involve global measures such as global timeouts or reset procedures become increasingly unaffordable, since their cost grows with the size of the network. Rather, for a fault handling mechanism to scale to large networks, its cost m ..."
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Cited by 63 (16 self)
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As communication networks grow, existing fault handling tools that involve global measures such as global timeouts or reset procedures become increasingly unaffordable, since their cost grows with the size of the network. Rather, for a fault handling mechanism to scale to large networks, its cost must depend only on the number of failed nodes Žwhich, thanks to today’s technology, grows much more slowly than the networks.. Moreover, it should allow the nonfaulty regions of the networks to continue their operation even during the recovery of the faulty parts. This paper introduces the concepts fault locality and faultlocally mendable problems, which are problems for which there are correction algorithms Žapplied after faults. whose cost depends only on the Ž unknown. number of faults. We show that any inputoutput problem is faultlocally mendable. The solution involves a novel technique combining data structures and ‘‘local votes’ ’ among nodes, which may be of interest in itself. � 1999 Academic Press * Alexander Goldberg lecturer.
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 59 (13 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
Hundreds of Impossibility Results for Distributed Computing
 Distributed Computing
, 2003
"... We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refe ..."
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Cited by 44 (4 self)
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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing.
Local Stabilizer
 In Proceedings of the 5th Israel Symposium on Theory of Computing and Systems
, 1997
"... A local stabilizer protocol that takes any online or offline distributed algorithm and converts it into a synchronous selfstabilizing algorithm with local monitoring and repairing properties is presented. Whenever the selfstabilizing version enters an inconsistent state, the inconsistency is ..."
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Cited by 35 (1 self)
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A local stabilizer protocol that takes any online or offline distributed algorithm and converts it into a synchronous selfstabilizing algorithm with local monitoring and repairing properties is presented. Whenever the selfstabilizing version enters an inconsistent state, the inconsistency is detected, in O(1) time, and the system state is repaired in a local manner. The expected computation time that is lost during the repair process is proportional to the largest diameter of a faulty region. An extended abstract of this paper appeared in the Proc. of the 5th Israeli Symposium on Theory of Computing and Systems, June 1997 and a brief announcement in Proc. of the 16th Annual ACM Symp. on Principles of Distributed Computing, August 1997. y Computer Science Department, TelAviv University, TelAviv, 69978, Israel. Email: afek@math.tau.ac.il. z Department of Mathematics and Computer Science, BenGurion University, BeerSheva, 84105, Israel. Partially supported by the Israeli m...
Computing Anonymously with Arbitrary Knowledge
 In Proceedings of the 18th ACM Symposium on principles of distributed computing
, 1999
"... We provide characterizations of the relations that can be computed with arbitrary knowledge on networks where all processors use the same algorithm and start from the same state (in particular, we do not assume that a bound on the network size is known). Three activation models are considered (synch ..."
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Cited by 25 (2 self)
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We provide characterizations of the relations that can be computed with arbitrary knowledge on networks where all processors use the same algorithm and start from the same state (in particular, we do not assume that a bound on the network size is known). Three activation models are considered (synchronous, asynchronous, interleaved) . 1 Introduction The question concerning which problems can be solved by a distributed system when all processors use the same algorithm and start from the same state has a long story: it was firstly formulated by Angluin [1], who investigated the problem of establishing a "center". She was the first to realize the connection with the theory of graph coverings, which was going to provide, in particular with the work of Yamashita and Kameda [11], several characterization for problems that are solvable under certain topological constraints. Further investigation led to the classification of computable functions [11, 10, 3, 9], and allowed to eliminate severa...
An Effective Characterization of Computability in Anonymous Networks
 In Distributed Computing, 15th International Symposium
"... We provide effective (i.e., recursive) characterizations of the relations that can be computed on networks where all processors use the same algorithm, start from the same state, and know at least a bound on the network size. Three activation models are considered (synchronous, asynchronous, inte ..."
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Cited by 25 (1 self)
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We provide effective (i.e., recursive) characterizations of the relations that can be computed on networks where all processors use the same algorithm, start from the same state, and know at least a bound on the network size. Three activation models are considered (synchronous, asynchronous, interleaved).
The Local Detection Paradigm and its Applications to SelfStabilization
"... A new paradigm for the design of selfstabilizing distributed algorithms, called local detection, is introduced. The essence of the paradigm is in defining a local condition based on the state of a processor and its immediate neighborhood, such that the system is in a globally legal state if and onl ..."
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Cited by 24 (8 self)
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A new paradigm for the design of selfstabilizing distributed algorithms, called local detection, is introduced. The essence of the paradigm is in defining a local condition based on the state of a processor and its immediate neighborhood, such that the system is in a globally legal state if and only if the local condition is satisfied at all the nodes. In this work we also extend the model of selfstabilizing networks traditionally assuming memory failure to include the model of dynamic networks (assuming edge failures and recoveries). We apply the paradigm to the extended model which we call "dynamic selfstabilizing networks. " Without loss of generality, we present the results in the least restrictive shared memory model of read/write atomicity, to which end we construct basic information transfer primitives. Using local detection, we develop deterministic and randomized selfstabilizing algorithms that maintain a rooted spanning tree in a general network whose topology changes dynamically. The deterministic algorithm assumes unique identities while the randomized assumes an anonymous network. The algorithms use a constant number of memory words per edge in each node; and both The size of memory words and of messages is the number of bits necessary to represent a node identity (typically O(log n) bits where n is the size of the network). These algorithms provide for the easy construction of selfstabilizing protocols for numerous tasks: reset, routing, topologyupdate and selfstabilization transformers that automatically selfstabilize existing protocols for which local detection conditions can be defined.