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23
Compass Routing on Geometric Networks
 IN PROC. 11 TH CANADIAN CONFERENCE ON COMPUTATIONAL GEOMETRY
, 1999
"... In this paper we study local routing algorithms on geometric networks. Formally speaking, suppose that we want to travel from a vertex s to a vertex t of a geometric network. A routing algorithm is called a local routing algorithm if it satisfies the following conditions: ..."
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Cited by 266 (14 self)
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In this paper we study local routing algorithms on geometric networks. Formally speaking, suppose that we want to travel from a vertex s to a vertex t of a geometric network. A routing algorithm is called a local routing algorithm if it satisfies the following conditions:
Compact routing schemes
 in SPAA ’01: Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
"... We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extrem ..."
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Cited by 196 (7 self)
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We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extremely short. The routing decision at each node takes constant time. Yet, the stretch of these routing schemes, i.e., the worst ratio between the cost of the path on which a packet is routed and the cost of the cheapest path from source to destination, is a small constant. Our schemes achieve a nearoptimal tradeoff between the size of the routing tables used and the resulting stretch. More specifically, we obtain: 1. A routing scheme that uses only ~ O(n 1=2) bits of memory at each node of an nnode network that has stretch 3. The space is optimal, up to logarithmic factors, in the sense that
Compact and Localized Distributed Data Structures
 JOURNAL OF DISTRIBUTED COMPUTING
, 2001
"... This survey concerns the role of data structures for compactly storing and representing various types of information in a localized and distributed fashion. Traditional approaches to data representation are based on global data structures, which require access to the entire structure even if the sou ..."
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Cited by 72 (25 self)
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This survey concerns the role of data structures for compactly storing and representing various types of information in a localized and distributed fashion. Traditional approaches to data representation are based on global data structures, which require access to the entire structure even if the sought information involves only a small and local set of entities. In contrast, localized data representation schemes are based on breaking the information into small local pieces, or labels, selected in a way that allows one to infer information regarding a small set of entities directly from their labels, without using any additional (global) information. The survey focuses on combinatorial and algorithmic techniques, and covers complexity results on various applications, including compact localized schemes for message routing in communication networks, and adjacency and distance labeling schemes.
Compact Routing Tables for Graphs of Bounded Genus
, 2000
"... This paper deals with compact shortest path routing tables on weighted graphs with n nodes. For planar graphs we show how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log 2+ n) bitoperations per node to extract the route, for any constant > 0. ..."
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Cited by 31 (13 self)
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This paper deals with compact shortest path routing tables on weighted graphs with n nodes. For planar graphs we show how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log 2+ n) bitoperations per node to extract the route, for any constant > 0. We obtain the same bounds for graphs of crossingedge number bounded by o(n= log n), and we generalize for graphs of genus bounded by > 0 yielding a size of n log +O(n) bits per node. Actually we prove a sharp upper bound of 2n log k +O(n) for graphs of pagenumber k, and a lower bound of n log k o(n log k) bits. These results are obtained by the use of dominating sets, compact coding of noncrossing partitions, and kpage representation of graphs.
Improved Compact Routing Scheme for Chordal Graphs
 IN 16 TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING (DISC
, 2002
"... This paper concerns routing with succinct tables in chordal graphs. We show how to construct in polynomial time, for every nnode chordal graph, a routing scheme using routing tables and addresses of O(log³ n/ log log n) bits per node, and O(log² n/ log log n) bit not alterable headers such that ..."
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Cited by 13 (6 self)
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This paper concerns routing with succinct tables in chordal graphs. We show how to construct in polynomial time, for every nnode chordal graph, a routing scheme using routing tables and addresses of O(log³ n/ log log n) bits per node, and O(log² n/ log log n) bit not alterable headers such that the length of the route between any two nodes is at most the distance between the nodes in the graph plus two.
Interval Routing Schemes allow Broadcasting with Linear MessageComplexity
, 2000
"... 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 an ..."
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Cited by 11 (4 self)
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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.
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 ..."
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Cited by 6 (2 self)
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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
DeadlockFree Routing in Irregular Networks Using Prefix Routing
 IN PROCEEDINGS OF PARALLEL AND DISTRIBUTED COMPUTING SYSTEMS
, 1999
"... In this paper, we propose a deadlockfree routing in irregular networks using prefix routing. Prefix routing is a special type of routing with a compact routing table associated with each node (processor). Basically, each outgoing channel of a node is assigned a special label and an outgoing channel ..."
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Cited by 6 (2 self)
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In this paper, we propose a deadlockfree routing in irregular networks using prefix routing. Prefix routing is a special type of routing with a compact routing table associated with each node (processor). Basically, each outgoing channel of a node is assigned a special label and an outgoing channel is selected if its label is a prefix of the label of the destination node. Node and channel labeling in an irregular network is done through constructing a spanning tree. The routing process follows a twophase process of going up and then down along the spanning tree, with a possible cross channel (shortcut) between two branches of the tree between two phases. We show that the proposed routing scheme is deadlock and livelock free. Possible extensions are also discussed.
Compact Routing Schemes for Generalised Chordal Graphs
, 2004
"... In this paper, we show how to use the notion of layeringtree introduced in [5], in order to obtain polynomial time constructible routing schemes. We describe efficient routing schemes for two classes of graphs that include the class of chordal graphs. For kchordal graphs, i.e., graphs containing n ..."
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Cited by 5 (0 self)
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In this paper, we show how to use the notion of layeringtree introduced in [5], in order to obtain polynomial time constructible routing schemes. We describe efficient routing schemes for two classes of graphs that include the class of chordal graphs. For kchordal graphs, i.e., graphs containing no induced cycle of length greater than k, the routing scheme uses addresses and local memories of size O(log 2 n) bits per node, and the length of the route between all pairs of vertices never exceeds their distance plus k + 1 (deviation at most k + 1). For treelength δ graphs, i.e., graphs admitting a treedecomposition in which the diameter of any bag is at most δ, the routing scheme uses addresses and local memories of size O(δ log 2 n) bits per node, and its deviation is at most 6δ −2. Observe that for chordal graphs, for which δ = 1 and k = 3, both schemes produce a deviation 4, with addresses and local memories of size O(log 2 n)bitsper node.
Interval Routing in Reliability Networks
, 2003
"... In this paper we consider routing with compact tables in reliability networks. ..."
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Cited by 4 (2 self)
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In this paper we consider routing with compact tables in reliability networks.