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Proof Labeling Schemes
 Proc. the 24th Annual ACM Symposium on Principles of Distributed Computing (PODC 2005), Las Vegas
, 2005
"... This paper addresses the problem of locally verifying global properties. Several natural questions are studied, such as “how expensive is local verification? ” and more specifically “how expensive is local verification compared to computation? ” A suitable model is introduced in which these questio ..."
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Cited by 20 (13 self)
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This paper addresses the problem of locally verifying global properties. Several natural questions are studied, such as “how expensive is local verification? ” and more specifically “how expensive is local verification compared to computation? ” A suitable model is introduced in which these questions are studied in terms of the number of bits a node needs to communicate. In addition, approaches are presented for the efficient construction of schemes, and upper and lower bounds are established on the cost of schemes for multiple basic problems. The paper also studies the role and cost of unique identities in terms of impossibility and complexity. Previous studies on related questions deal with distributed algorithms that simultaneously compute a configuration and verify that this configuration has a certain desired property. It turns out that this combined approach enables verification to be less costly, since the configuration is typically generated so as to be easily verifiable. In contrast, our approach separates the configuration design from the verification. That is, it first generates the desired configuration without bothering with the need to verify, and then handles the task of constructing a suitable verification scheme. Our approach thus allows for a more modular design of algorithms, and has the potential to aid in verifying properties even when the original design of the structures for maintaining them was done without verification in mind.
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.
A SketchBased Distance Oracle for WebScale Graphs
"... We study the fundamental problem of computing distances between nodes in large graphs such as the web graph and social networks. Our objective is to be able to answer distance queries between pairs of nodes in real time. Since the standard shortest path algorithms are expensive, our approach moves t ..."
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Cited by 16 (1 self)
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We study the fundamental problem of computing distances between nodes in large graphs such as the web graph and social networks. Our objective is to be able to answer distance queries between pairs of nodes in real time. Since the standard shortest path algorithms are expensive, our approach moves the timeconsuming shortestpath computation offline, and at query time only looks up precomputed values and performs simple and fast computations on these precomputed values. More specifically, during the offline phase we compute and store a small “sketch ” for each node in the graph, and at querytime we look up the sketches of the source and destination nodes and perform a simple computation using these two sketches to estimate the distance. Categories and Subject Descriptors G.2.2 [Graph Theory]: Graph algorithms, path and circuit problems
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 16 (9 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.
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
Labellng Schemes for Tree Representation
"... This paper deals with compact labelbased representations for trees. Consider an nnode undirected connected graph G with a predefined numbering on the ports of each node. The allports tree labeling Lall gives each node v of G a label containing the port numbers of all the tree edges incident to v. ..."
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This paper deals with compact labelbased representations for trees. Consider an nnode undirected connected graph G with a predefined numbering on the ports of each node. The allports tree labeling Lall gives each node v of G a label containing the port numbers of all the tree edges incident to v. The upward tree labeling Lup labels each node v by the number of the port leading from v to its parent in the tree. Our measure of interest is the worst case and total length of the labels used by the scheme, denoted Mup(T) and Sup(T) for Lup and Mall(T) and Sall(T) for Lall. The problem studied in this paper is the following: Given a graph G and a predefined port labeling for it, with the ports of each node v numbered by 0,...,deg(v) − 1, select a rooted spanning tree for G minimizing (one of) these measures. We show that the problem is polynomial for Mup(T), Sup(T) and Sall(T) but NPhard for Mall(T) (even for 3regular planar graphs). We show that for every graph G and port labeling there exists a spanning tree T for which Sup(T) = O(n log log n). We give a tight bound of O(n) in the cases of complete graphs with arbitrary labeling and arbitrary graphs with symmetric port labeling. We conclude by discussing some applications for our tree representation schemes.
• Postdoctoral Students
, 2008
"... Searching and dissemination of information on largescale platforms ProjectTeam proposal – CR Bordeaux SudOuest ..."
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Searching and dissemination of information on largescale platforms ProjectTeam proposal – CR Bordeaux SudOuest
THE EATCS COLUMNS Computing with Advice: when Knowledge Helps
"... In several areas of computer science the possibility and efficiency of the solution is determined by information that is not accessible to the algorithm. Traditionally, a qualitative approach to the study of this information has been pursued, in which the impact of enhancing the algorithm with vario ..."
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In several areas of computer science the possibility and efficiency of the solution is determined by information that is not accessible to the algorithm. Traditionally, a qualitative approach to the study of this information has been pursued, in which the impact of enhancing the algorithm with various specific types of information has been studied. Recently, a number of authors have proposed a quantitative approach, where the amount of the added information is studied in relation with the improvement of the quality or efficiency of the solution. We survey several recent examples of this approach from the area of distributed and online computing. 1
Oracle Size: A new measure of . . .
, 2006
"... We study the problem of the amount of knowledge about a communication network that must be given to its nodes in order to efficiently disseminate information. While previous results about communication in networks used particular partial information available to nodes, such as the knowledge of the n ..."
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We study the problem of the amount of knowledge about a communication network that must be given to its nodes in order to efficiently disseminate information. While previous results about communication in networks used particular partial information available to nodes, such as the knowledge of the neighborhood or the knowledge of the network topology within some radius, our approach is quantitative: we investigate the minimum total number of bits of information (minimum oracle size) that has to be available to nodes in order to perform efficient communication. It turns out that the minimum oracle size for which a distributed task can be accomplished efficiently, can serve as a measure of the difficulty of this task. We use this measure to make a quantitative distinction between the difficulty of