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The geometry of graphs and some of its algorithmic applications
 COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
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Cited by 524 (19 self)
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that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that distances between vertices in G closely match the distances between
Similarity Flooding: A Versatile Graph Matching Algorithm and Its Application to Schema Matching
, 2002
"... Matching elements of two data schemas or two data instances plays a key role in data warehousing, ebusiness, or even biochemical applications. In this paper we present a matching algorithm based on a fixpoint computation that is usable across different scenarios. The algorithm takes two graphs (sch ..."
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Cited by 592 (12 self)
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Matching elements of two data schemas or two data instances plays a key role in data warehousing, ebusiness, or even biochemical applications. In this paper we present a matching algorithm based on a fixpoint computation that is usable across different scenarios. The algorithm takes two graphs
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige, Goldwasser, Lovász, Safra and Szegedy [42], and Arora and Safra [6] and shows that there exists a positive ɛ such that approximating
Selfstabilization with Path Algebra
 Theoretical Computer Science
, 2003
"... Selfstabilizing protocols can resist transient failures and guarantee system recovery in a finite time. We highlight the connexion between the formalism of selfstabilizing distributed systems and the formalism of generalised path algebra and asynchronous iterations with delay. We use the later to ..."
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Cited by 7 (1 self)
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to prove that a local condition on locally executed algorithm (being a strictly idempotent roperator) ensures selfstabilization of the global system. As a result, a parametrized distributed algorithm applicable to any directed graph topology is proposed, and the function parameter of our algorithm
Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 446 (2 self)
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This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper
Patterns for Routing and SelfStabilization
 in Proc. of Network Operations & Management Symposium (NOMS 2004), Seoul, Korea
, 2004
"... This paper contributes towards engineering selfstabilizing networks and services. We propose the use of navigation patterns, which define how information for state updates is disseminated in the system, as fundamental building blocks for selfstabilizing systems. We present two navigation patterns f ..."
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Cited by 7 (2 self)
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This paper contributes towards engineering selfstabilizing networks and services. We propose the use of navigation patterns, which define how information for state updates is disseminated in the system, as fundamental building blocks for selfstabilizing systems. We present two navigation patterns
Selfstabilization with roperators
 Distributed Computing
, 2001
"... this work can be found in [17]. ..."
SelfStabilizing Diffusion
, 1997
"... This paper deals with a peculiar instance of the consensus problem. In our scenario, the system can be assimilated to an irregular network composed of clusters of processing units. Each unit holds a ”copy ” of a value, that changes continuously according with a known function. The basic problem we a ..."
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This paper deals with a peculiar instance of the consensus problem. In our scenario, the system can be assimilated to an irregular network composed of clusters of processing units. Each unit holds a ”copy ” of a value, that changes continuously according with a known function. The basic problem we address is to keep all the copies sufficiently close to the real value, given that most units cannot keep the local copy of the value exactly updated, with a minimal computational load. With respect to the ”precision ” of the local copy of the global value, we distinguish two kinds of units: a restricted number of units that continuously keep the correct value, upon which any other unit should agree, and the rest of the units, that can only estimate locally the current global value. We do not investigate the way in which the former units keep their copies exactly updated: since we count a few units of this kind in the system, they may use an expensive strategy. On the contrary, we are interested in the behavior of the rest of the system. The precision of the local estimate of the other units progressively degrades, and they need to periodically refresh their local estimate in order to keep it acceptably near to the global value. Our problem is the design of a protocol that performs this task. The relevance of the problem should become evident if we recognize that the above description is a paraphrase of the clock synchronization problem: a few units in the system hold accurate (and expensive) clocks, while the others periodically synchronize their inaccurate (and cheap) clocks with the accurate ones. The interested reader can find a technical discussion of the problem and its practical solution in Internet in [7]: the protocol suite is known as Network Time
Selfstabilization with Path Algebra
, 2011
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Introducing Recurrence in SelfStabilization?
, 2014
"... Copyright c © July 2014 by the author(s) ..."
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