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86
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
Initializing Newly Deployed Ad Hoc and Sensor Networks
 in Proceedings of 10 th Annual International Conference on Mobile Computing and Networking (MOBICOM
, 2004
"... A newly deployed multihop radio network is unstructured and lacks a reliable and e#cient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multihop quasi ..."
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Cited by 50 (15 self)
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A newly deployed multihop radio network is unstructured and lacks a reliable and e#cient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multihop quasi unit disk graph and allow nodes to wake up asynchronously at any time. Further, nodes do not feature a reliable collision detection mechanism, and they have only limited knowledge about the network topology. We show that even for this restricted model, a good clustering can be computed e#ciently. Our algorithm e#ciently computes an asymptotically optimal clustering. Based on this algorithm, we describe a protocol for quickly establishing synchronized sleep and listen schedule between nodes within a cluster. Additionally, we provide simulation results in a variety of settings.
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.
Maximal Independent Sets in Radio Networks
"... We study the distributed complexity of computing a maximal independent set (MIS) in radio networks with completely unknown topology, asynchronous wakeup, and no collision detection mechanism available. Specifically, we propose a novel randomized algorithm that computes a MIS in time O(log 2 n) with ..."
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Cited by 37 (8 self)
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We study the distributed complexity of computing a maximal independent set (MIS) in radio networks with completely unknown topology, asynchronous wakeup, and no collision detection mechanism available. Specifically, we propose a novel randomized algorithm that computes a MIS in time O(log 2 n) with high probability, where n is the number of nodes in the network. This significantly improving on the best previously known solutions. A lower bound of Ω(log 2 n / log log n) given in [11] implies that our algorithm’s running time is close to optimal. Our result shows that the harsh radio network model imposes merely an additional O(log n) factor compared to Luby’s MIS algorithm in the message passing model. This has important implications in the context of ad hoc and sensor networks whose characteristics are closely captured by the radio network model.
Modeling sensor networks
, 2008
"... In order to develop algorithms for sensor networks and in order to give mathematical correctness and performance proofs, models for various aspects of sensor networks are needed. This chapter presents and discusses currently used models for sensor networks. Generally, finding good models is a challe ..."
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Cited by 27 (5 self)
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In order to develop algorithms for sensor networks and in order to give mathematical correctness and performance proofs, models for various aspects of sensor networks are needed. This chapter presents and discusses currently used models for sensor networks. Generally, finding good models is a challenging task. On the one hand, a
Facility location: distributed approximation
 In Proceedings of the twentyfourth annual ACM symposium on Principles of distributed computing
, 2005
"... In this paper, we initiate the study of the approximability of the facility location problem in a distributed setting. In particular, we explore a tradeoff between the amount of communication and the resulting approximation ratio. We give a distributed algorithm that, for every constant k, achieves ..."
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Cited by 27 (1 self)
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In this paper, we initiate the study of the approximability of the facility location problem in a distributed setting. In particular, we explore a tradeoff between the amount of communication and the resulting approximation ratio. We give a distributed algorithm that, for every constant k, achieves an O ( √ k(mρ) 1/ √ k log (m + n)) approximation in O(k) communication rounds where message size is bounded to O(log n) bits. The number of facilities and clients are m and n, respectively, and ρ is a coefficient that depends on the cost values of the instance. Our technique is based on a distributed primaldual approach for approximating a linear program, that does not form a covering or packing program.
Multihop local pooling for distributed throughput maximization in wireless networks
 in IEEE INFOCOM
, 2008
"... Abstract—Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary or secondaryinterference constraints have been developed. Due to their distributed operatio ..."
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Cited by 23 (8 self)
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Abstract—Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary or secondaryinterference constraints have been developed. Due to their distributed operation, these algorithms can achieve only a guaranteed fraction of the maximum possible throughput. It was also recently shown that if a set of conditions (known as Local Pooling) is satisfied, simple distributed scheduling algorithms achieve 100 % throughput. However, previous work conditions and on networks with singlehop interference or singlehop traffic. In this paper, we identify several graph classes that satisfy the Local Pooling conditions, thereby enabling the use of such graphs in network design algorithms. Then, we study the multihop implications of Local Pooling. We show that in many cases, as the interference degree increases, the Local Pooling conditions are more likely to hold. Consequently, although increased interference reduces the maximum achievable throughput of the network, it tends to enable distributed algorithms to achieve 100 % of this throughput. Regarding multihop traffic, we show that if the network satisfies only the singlehop Local Pooling conditions, distributed joint routing and scheduling algorithms are not guaranteed to achieve maximum throughput. Therefore, we present new conditions for Multihop Local Pooling, under which distributed algorithms achieve 100 % throughout. Finally, we identify network topologies in which the conditions hold and discuss the algorithmic implications of the results.
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 MST Computation with Short Advice
 SPAA
, 2007
"... We use the recently introduced advising scheme framework for measuring the difficulty of locally distributively computing a Minimum Spanning Tree (MST). An (m, t)advising scheme for a distributed problem P is a way, for every possible input I of P, to provide an ”advice” (i.e., a bit string) about ..."
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Cited by 21 (10 self)
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We use the recently introduced advising scheme framework for measuring the difficulty of locally distributively computing a Minimum Spanning Tree (MST). An (m, t)advising scheme for a distributed problem P is a way, for every possible input I of P, to provide an ”advice” (i.e., a bit string) about I to each node so that: (1) the maximum size of the advices is at most m bits, and (2) the problem P can be solved distributively in at most t rounds using the advices as inputs. In case of MST, the output returned by each node of a weighted graph G is the edge leading to its parent in some rooted MST T of G. Clearly, there is a trivial (⌈log n⌉, 0)advising scheme for MST (each node is given the local port number of the edge leading to the root of some MST T), and it is known that any (0, t)advising scheme satisfies t ≥ ˜ Ω ( √ n). Our main result is the construction of an (O(1), O(log n))advising scheme for MST. That is, by only giving a constant number of bits of advice to each node, one can decrease exponentially the distributed computation time of MST in arbitrary graph, compared to algorithms dealing with the problem in absence of any a priori information. We also consider the average size of the advices. On the one hand, we show that any (m, 0)advising scheme for MST gives advices of average size Ω(log n). On the other hand we design an (m, 1)advising scheme for MST with advices of constant average size, that is one round is enough to decrease the average size of the advices from log n to constant.