Results 1 
9 of
9
Routing in Distributed Networks: Overview and Open Problems
 ACM SIGACT News  Distributed Computing Column
, 2001
"... This article focuses on routing messages in distributed networks with efficient data structures. After an overview of the various results of the literature, we point some interestingly open problems. ..."
Abstract

Cited by 49 (12 self)
 Add to MetaCart
This article focuses on routing messages in distributed networks with efficient data structures. After an overview of the various results of the literature, we point some interestingly open problems.
Finding Short RightHandontheWall Walks in Graphs
 In SIROCCO
, 2005
"... Abstract. We consider the problem of perpetual traversal by a single agent in an anonymous undirected graph G. Our requirements are: (1) deterministic algorithm, (2) each node is visited within O(n) moves,(3) the agent uses no memory, it can use only the label of the link via which it arrived to the ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
Abstract. We consider the problem of perpetual traversal by a single agent in an anonymous undirected graph G. Our requirements are: (1) deterministic algorithm, (2) each node is visited within O(n) moves,(3) the agent uses no memory, it can use only the label of the link via which it arrived to the current node, (4) no marking of the underlying graph is allowed and (5) no additional information is stored in the graph (e.g. routing tables, spanning tree) except the ability to distinguish between the incident edges (called Local Orientation). This problem is unsolvable, as has been proven in [9, 28] even for much less restrictive setting. Our approach is to somewhat relax the requirement (5). We fix the following traversal algorithm: “Start by taking the edge with the smallest label. Afterwards, whenever you come to a node, continue by taking the successor edge (in the local orientation) to the edge via which you arrived ” and ask whether it is for every undirected graph possible to assign the local orientations in such a way that the resulting perpetual traversal visits every node in O(n) moves. We give a positive answer to this question, by showing how to construct such local orientations. This leads to an extremely simple, memoryless, yet efficient traversal algorithm. 1
Theory of BAR games
 In Brief Announcements: Proceedings of the Symposium on Principles of Distributed Computing (PODC 2007
, 2006
"... Distributed systems that span multiple administrative domains require protocols that tolerate both Byzantine and selfish nodes. This paper offers a theory that can be used to analyze such protocols. The theory systematically extends traditional game theory solution concepts through an ex ante analys ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
Distributed systems that span multiple administrative domains require protocols that tolerate both Byzantine and selfish nodes. This paper offers a theory that can be used to analyze such protocols. The theory systematically extends traditional game theory solution concepts through an ex ante analysis that incorporates a rational player’s awareness of the possible presence of Byzantine players in the player’s utility function. We illustrate our approach by modeling synchronous Terminating Reliable Broadcast as a game. We show that Dolev and Strong’s Byzantine TRB protocol with message authentication is not a Nash equilibrium and that rational deviations from it may lead to violation of the TRB safety properties. We present a new TRB protocol with the same asymptotic complexity of DolevStrong and prove it to be a Nash equilibrium. Finally, we prove that (kt) robustness, a recently proposed solution concept for games with Byzantine and rational players, cannot yield an equilibrium in games, such as our TRB game, that model systems where any node may crash and communication is necessary and incurs cost. 1
Geometric routing without geometry
 in 12th Colloquium on Structural Information and Communication Complexity. MontStMichel
, 2005
"... In this paper we propose a new routing paradigm, called pseudogeometric routing. In pseudogeometric routing, each node u of a network of computing elements is assigned a pseudo coordinate composed of the graph (hop) distances from u to a set of designated nodes (the anchors) in the network. On the ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
In this paper we propose a new routing paradigm, called pseudogeometric routing. In pseudogeometric routing, each node u of a network of computing elements is assigned a pseudo coordinate composed of the graph (hop) distances from u to a set of designated nodes (the anchors) in the network. On theses pseudo coordinates we employ greedy geometric routing. Almost as a side effect, pseudogeometric routing is not restricted to planar unit disk graph networks anymore, but succeeds on general networks. 1
Memory Efficient Anonymous Graph Exploration
 In Proc. WG’08, LNCS
, 2008
"... Abstract. Efficient exploration of unknown or unmapped environments has become one of the fundamental problem domains in algorithm design. Its applications range from robot navigation in hazardous environments to rigorous searching, indexing and analysing digital data available on the Internet. A la ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Abstract. Efficient exploration of unknown or unmapped environments has become one of the fundamental problem domains in algorithm design. Its applications range from robot navigation in hazardous environments to rigorous searching, indexing and analysing digital data available on the Internet. A large number of exploration algorithms has been proposed under various assumptions about the capability of mobile (exploring) entities and various characteristics of the environment which are to be explored. This paper considers the graph model, where the environment is represented by a graph of connections in which discrete moves are permitted only along its edges. Designing efficient exploration algorithms in this model has been extensively studied under a diverse set of assumptions, e.g., directed vs undirected graphs, anonymous nodes vs nodes with distinct identities, deterministic vs probabilistic solutions, single vs multiple agent exploration, as well as in the context of different complexity measures including the time complexity, the memory consumption, and the use of other computational resources such as tokens and messages. In this work the emphasis is on memory efficient exploration of anonymous graphs. We discuss in more detail three approaches: random walk, Propp machine and basic walk, reviewing major relevant results, presenting recent developments, and commenting on directions for further research. 1
Distributed Mobile Computing with Incomparable Labels
"... An obvious focus of mobile computing is the issue of computability in a distributed mobile environment, in particular determining what minimal hypotheses allow a given problem to be solved by a set of mobile entities (agents) moving in a network. For instance, there is no universal, nor even effecti ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
An obvious focus of mobile computing is the issue of computability in a distributed mobile environment, in particular determining what minimal hypotheses allow a given problem to be solved by a set of mobile entities (agents) moving in a network. For instance, there is no universal, nor even effective, election algorithm if both the agents and the network are anonymous. On the other hand, if agents or nodes are labeled with distinct elements which are comparable (i.e., from a totally ordered set), then a universal (an hence effective) election algorithm does exist. In other words, distinctness is a necessary condition...
Electing a Leader Among Anonymous Mobile Agents in Anonymous Networks With SenseofDirection
, 2002
"... We consider a collection of r anonymous asynchronous mobile agents dispersed on an arbitrary anonymous network of size n. Neither r nor n are known a priori by the agents. We examine the problem of electing a leader among those agents and study the conditions for its solvability. We show that, wi ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
We consider a collection of r anonymous asynchronous mobile agents dispersed on an arbitrary anonymous network of size n. Neither r nor n are known a priori by the agents. We examine the problem of electing a leader among those agents and study the conditions for its solvability. We show that, without sense of direction, the problem is unsolvable (even if gcd(r; n) = 1). We also show that, with sense of direction, the problem is solvable if and only if gcd(r; n) = 1. The possibility proof is constructive, and the proposed protocol is novel and ecient.
Setting Port Numbers for Fast Graph Exploration
"... Abstract. We consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of arbitrary size and arbitrary maximum degree. In anonymous graphs, nodes are not labeled but edges are labeled in ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Abstract. We consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of arbitrary size and arbitrary maximum degree. In anonymous graphs, nodes are not labeled but edges are labeled in a local manner (called local orientation) sothat the automaton is able to distinguish them. Precisely, the edges incident toanodev are given port numbers from 1 to dv, wheredv is the degree of v. Periodic graph exploration means visiting every node infinitely often. We are interested in the length of the period, i.e., the maximum number of edge traversals between two consecutive visits of any node by the automaton in the same state and entering the node by the same port. This problem is unsolvable if local orientations are set arbitrarily. Given this impossibility result, we address the following problem: what is the mimimum function π(n) such that there exist an algorithm for setting the local orientation, and a finite automaton using it, such that the automaton explores all graphs of size n within the period π(n)? The best result so far is the upper bound π(n) ≤ 10n, byDobrev et al. [SIROCCO 2005], using an automaton with no memory (i.e. only one state). In this paper we prove a better upper bound π(n) ≤ 4n. Our automaton uses three states but performs periodic exploration independently of its starting position and initial state. 1
Interval Routing Schemes allow Broadcasting with Linear MessageComplexity (Extended Abstract)
, 2000
"... ] Pierre Fraigniaud y Cyril Gavoille z Bernard Mans x ABSTRACT The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required ..."
Abstract
 Add to MetaCart
] Pierre Fraigniaud y Cyril Gavoille z Bernard Mans x ABSTRACT The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required to store the routing tables as small as possible. In this paper, we answer a longstanding conjecture by showing that compact routing can also help to perform distributed computations. In particular, we show that a network supporting a shortest path interval routing scheme allows to broadcast with an O(n) messagecomplexity, where n is the number of nodes of the network. As a consequence, we prove that O(n) messages suce to solve leaderelection for any graph labeled by a shortest path interval routing scheme, improving therefore the O(m + n) previous known bound. Keywords: Compact routing, Interval routing, Broadcasting, Distributed computing. 1. INTRODUCTION This paper addresses a prob...