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46
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 112 (27 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.
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 69 (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
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 18 (9 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.
Linear lower bounds on realworld implementations of concurrent objects
 In Proceedings of the 46th Annual Symposium on Foundations of Computer Science (FOCS
, 2005
"... Abstract This paper proves \Omega (n) lower bounds on the time to perform a single instance of an operationin any implementation of a large class of data structures shared by n processes. For standarddata structures such as counters, stacks, and queues, the bound is tight. The implementations consid ..."
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Cited by 15 (10 self)
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Abstract This paper proves \Omega (n) lower bounds on the time to perform a single instance of an operationin any implementation of a large class of data structures shared by n processes. For standarddata structures such as counters, stacks, and queues, the bound is tight. The implementations considered may apply any deterministic primitives to a base object. No bounds are assumedon either the number of base objects or their size. Time is measured as the number of steps a process performs on base objects and the number of stalls it incurs as a result of contentionwith other processes. 1
Networks Cannot Compute Their Diameter in Sublinear Time preliminary version please check for updates
, 2011
"... We study the problem of computing the diameter of a network in a distributed way. The model of distributed computation we consider is: in each synchronous round, each node can transmit a different (but short) message to each of its neighbors. We provide an ˜ Ω(n) lower bound for the number of commun ..."
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Cited by 11 (2 self)
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We study the problem of computing the diameter of a network in a distributed way. The model of distributed computation we consider is: in each synchronous round, each node can transmit a different (but short) message to each of its neighbors. We provide an ˜ Ω(n) lower bound for the number of communication rounds needed, where n denotes the number of nodes in the network. This lower bound is valid even if the diameter of the network is a small constant. We also show that a (3/2 − ε)approximation of the diameter requires ˜ Ω ( √ n) rounds. Furthermore we use our new technique to prove an ˜ Ω ( √ n) lower bound on approximating the girth of a graph by a factor 2 − ε. Contact author:
GRAPH SEARCHING WITH ADVICE
, 2007
"... Fraigniaud et al. (2006) introduced a new measure of difficulty for a distributed task in a network. The smallest number of bits of advice of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper ..."
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Cited by 10 (3 self)
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Fraigniaud et al. (2006) introduced a new measure of difficulty for a distributed task in a network. The smallest number of bits of advice of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper deals with the number of bits of advice required to perform efficiently the graph searching problem in a distributed setting. In this variant of the problem, all searchers are initially placed at a particular node of the network. The aim of the team of searchers is to capture an invisible and arbitrarily fast fugitive in a monotone connected way, i.e., the cleared part of the graph is permanently connected, and never decreases while the search strategy is executed. We show that the minimum number of bits of advice permitting the monotone connected clearing of a network in a distributed setting is O(n log n), where n is the number of nodes of the network, and this bound is tight. More precisely, we first provide a labelling of the vertices of any graph G, using a total of O(n log n) bits, and a protocol using this labelling that enables clearing G in a monotone connected distributed way. Then, we show that this number of bits of advice is almost optimal: no protocol using an oracle providing o(n log n) bits of advice permits the monotone connected clearing of a network using the smallest number of searchers.
Relationships between broadcast and shared memory in reliable anonymous distributed systems
 IN: PROC. 18TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING, LNCS
, 2004
"... We study the power of reliable anonymous distributed systems, where processes do not fail, do not have identifiers, and run identical programmes. We are interested specifically in the relative powers of systems with different communication mechanisms: anonymous broadcast, readwrite registers, or r ..."
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Cited by 9 (0 self)
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We study the power of reliable anonymous distributed systems, where processes do not fail, do not have identifiers, and run identical programmes. We are interested specifically in the relative powers of systems with different communication mechanisms: anonymous broadcast, readwrite registers, or readwrite registers plus additional sharedmemory objects. We show that a system with anonymous broadcast can simulate a system of sharedmemory objects if and only if the objects satisfy a property we call idemdicence; this result holds regardless of whether either system is synchronous or asynchronous. Conversely, the key to simulating anonymous broadcast in anonymous shared memory is the ability to count: broadcast can be simulated by an asynchronous sharedmemory system that uses only counters, but readwrite registers by themselves are not enough. We further examine the relative power of different types and sizes of bounded counters and conclude with a nonrobustness result.
Communication Algorithms with Advice
, 2009
"... We study the amount of knowledge about a communication network that must be given to its nodes in order to efficiently disseminate information. Our approach is quantitative: we investigate the minimum total number of bits of information (minimum size of advice) that has to be available to nodes, reg ..."
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Cited by 7 (5 self)
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We study the amount of knowledge about a communication network that must be given to its nodes in order to efficiently disseminate information. Our approach is quantitative: we investigate the minimum total number of bits of information (minimum size of advice) that has to be available to nodes, regardless of the type of information provided. We compare the size of advice needed to perform broadcast and wakeup (the latter is a broadcast in which nodes can transmit only after getting the source information), both using a linear number of messages (which is optimal). We show that the minimum size of advice permitting the wakeup with a linear number of messages in a nnode network, is Θ(nlog n), while the broadcast with a linear number of messages can be achieved with advice of size O(n). We also show that the latter size of advice is almost optimal: no advice of size o(n) can permit to broadcast with a linear number of messages. Thus an
Local Algorithms for Dominating and Connected Dominating Sets of Unit Disk Graphs
, 2007
"... Many protocols in distributed computing make use of dominating and connected dominating sets, for example for broadcasting and the computation of routing. Ad hoc networks impose an additional requirement that algorithms for the construction of such sets should be local in the sense that each node of ..."
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Cited by 7 (3 self)
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Many protocols in distributed computing make use of dominating and connected dominating sets, for example for broadcasting and the computation of routing. Ad hoc networks impose an additional requirement that algorithms for the construction of such sets should be local in the sense that each node of the network should make decisions based only on the information obtained from nodes located a constant (independent of the size of the network) number of steps away from it. The focus of the present paper is on providing local, constant approximation, deterministic algorithms for the construction of dominating and connected dominating sets of a Unit Disk Graph (UDG) with location aware nodes (i.e., nodes that know their coordinates in the plane). The size of the constructed set, in the case of the dominating set, is shown to be 5 times the optimal, while for the connected dominating set 7.453 + ɛ the optimal, for any arbitrarily small ɛ> 0. These are the first local algorithms in the scientific literature whose time