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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
Competitive Online Routing in Geometric Graphs
 Theoretical Computer Science
, 2001
"... We consider online routing algorithms for finding paths between the vertices of plane graphs. ..."
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Cited by 34 (4 self)
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We consider online routing algorithms for finding paths between the vertices of plane graphs.
On Interval Routing Schemes and Treewidth
 and treewidth,inProceedings 21thInternationalWorkshoponGraphTheoreticConceptsinComputerScienceWG'95,M.Nagl,ed.,SpringerVerlag,LectureNotesin ComputerScience,vol.1017,1995,pp.181{186
, 1997
"... In this paper, we investigate which processor networks allow k label Interval Routing Schemes, under the assumption that costs of edges may vary. We show that for each fixed k 1, the class of graphs allowing such routing schemes is closed under minortaking in the domain of connected graphs, and he ..."
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Cited by 16 (8 self)
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In this paper, we investigate which processor networks allow k label Interval Routing Schemes, under the assumption that costs of edges may vary. We show that for each fixed k 1, the class of graphs allowing such routing schemes is closed under minortaking in the domain of connected graphs, and hence has a linear time recognition algorithm. This result connects the theory of compact routing with the theory of graph minors and treewidth. We show that every graph that does not contain K 2;r as a minor has treewidth at most 2r \Gamma 2. In case the graph is planar, this bound can be lowered to r + 2. As a consequence, graphs that allow klabel Interval Routing Schemes under dynamic cost edges have treewidth at most 4k, and treewidth at most 2k + 3 if they are planar. Similar results are shown for other types of Interval Routing Schemes.
A Lower Bound for Linear Interval Routing
 Networks
, 1996
"... Linear Interval Routing is a spaceefficient routing method for pointtopoint communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wraparound. A common way to measure the efficiency of such r ..."
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Cited by 8 (5 self)
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Linear Interval Routing is a spaceefficient routing method for pointtopoint communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wraparound. A common way to measure the efficiency of such routing methods is in terms of the maximal length of a path a message traverses. For Interval Routing the upper bound and lower bound on this quantity are 2D and 1:75D \Gamma 1, respectively, where D is the diameter of the network. We prove a lower bound of \Omega\Gamma D 2 ) on the length of a path a message traverses under Linear Interval Routing. We further extend the result by showing a connection between the efficiency of Linear Interval Routing and the bi diameter of the network. 1 Introduction In a communication network, where communication between nodes is accomplished by sending and receiving messages, a routing algorithm is employed to ensure that every message will reach its des...
HammockonEars Decomposition: A Technique for the Efficient Parallel Solution of Shortest Paths and Other Problems
 Theoretical Computer Science
, 1996
"... We show how to decompose efficiently in parallel any graph into a number, ~ fl, of outerplanar subgraphs (called hammocks) satisfying certain separator properties. Our work combines and extends the sequential hammock decomposition technique introduced by G. Frederickson and the parallel ear decom ..."
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Cited by 8 (5 self)
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We show how to decompose efficiently in parallel any graph into a number, ~ fl, of outerplanar subgraphs (called hammocks) satisfying certain separator properties. Our work combines and extends the sequential hammock decomposition technique introduced by G. Frederickson and the parallel ear decomposition technique, thus we call it the hammockonears decomposition. We mention that hammockonears decomposition also draws from techniques in computational geometry and that an embedding of the graph does not need to be provided with the input. We achieve this decomposition in O(logn log log n) time using O(n + m) CREW PRAM processors, for an nvertex, medge graph or digraph. The hammockonears decomposition implies a general framework for solving graph problems efficiently. Its value is demonstrated by a variety of applications on a significant class of (di)graphs, namely that of sparse (di)graphs. This class consists of all (di)graphs which have a ~ fl between 1 and \Theta(n...
A Theoretical Model for Routing Complexity
 IN TH INTERNATIONAL COLLOQUIUM ON STRUCTURAL INFORMATION & COMMUNICATION COMPLEXITY (SIROCCO), CARLETON SCIENTI
, 1998
"... This paper introduces a formal model for studying the complexity of routing in networks. The aim of this model is to capture both time complexity and space complexity. In particular, the model takes into account the input and output facilities of routers. A routing program is a RAMprogram with five ..."
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Cited by 2 (2 self)
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This paper introduces a formal model for studying the complexity of routing in networks. The aim of this model is to capture both time complexity and space complexity. In particular, the model takes into account the input and output facilities of routers. A routing program is a RAMprogram with five additional instructions that allow to handle incoming and outgoing headers, and input and output ports. One of these five additional instructions, called release, captures the possible use of hardware facilities to speed up routing. Using our model, we show that there are routing functions which, if compacted, would require an arbitrarily large computation time to be decoded. The latency is the sum of the time (in bitoperation) required at every intermediate node to establish the route. We also show that, in any nnode network of diameter D, the latency is bounded by O(D+ n 1=k logn), for every constant k 2. This latter result has to be compared with the latency of the routing tables wh...
Lower Bounds for Compact Routing (Extended Abstract)
 In 17th International Symposium on Theoretical Aspects of Computer Science
, 1995
"... In this paper we present lower bounds for compact routing schemes. We give (1) networks on n vertices which for any interval routing scheme,\Omega\Gamma n) routers of the network require\Omega\Gamma n) intervals on some outgoing link and (2) for each d 3, networks of maximal degree d which for ..."
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Cited by 1 (0 self)
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In this paper we present lower bounds for compact routing schemes. We give (1) networks on n vertices which for any interval routing scheme,\Omega\Gamma n) routers of the network require\Omega\Gamma n) intervals on some outgoing link and (2) for each d 3, networks of maximal degree d which for any interval routing scheme,\Omega\Gamma n) routers each require \Omega\Gamma n= log n) intervals on some outgoing link. Our results give the best known worstcase lower bounds for interval routing. For the case of universal routing schemes we give (3) networks on n vertices which for any near optimal routing scheme with stretch factor ! 2 a total of \Omega\Gamma n 2 ) memory bits are required, and (4) for each d 3, networks of maximal degree d for which any optimal (resp., near optimal) routing scheme (resp., with stretch factor ! 2) requires a total of \Omega\Gamma n 2 = log n) (resp. \Omega\Gamma n 2 = log 2 n)) memory bits. 1980 Mathematics Subject Classification: 68Q99 C...
Implicit Routing And Shortest Path Information (Extended Abstract)
 Proc. 2nd Colloquium on Structural Information & Communication Complexity (SIROCCO’95
, 1995
"... ) Evangelos Kranakis y (kranakis@scs.carleton.ca) Danny Krizanc y (krizanc@scs.carleton.ca) Jorge Urrutia zy (jorge@csi.uottawa.ca) Abstract We study the problem of constructing graphs from shortest path information (complete or partial). Consider graphs with labeled vertices and edges. Given ..."
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Cited by 1 (0 self)
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) Evangelos Kranakis y (kranakis@scs.carleton.ca) Danny Krizanc y (krizanc@scs.carleton.ca) Jorge Urrutia zy (jorge@csi.uottawa.ca) Abstract We study the problem of constructing graphs from shortest path information (complete or partial). Consider graphs with labeled vertices and edges. Given a collection V of vertices and for each u 2 V a positive integer d(u), and a family F u = fF u;i : i ! d(u)g of subsets of V construct a graph such that for each u and each link i of u, F u;i is the set of nodes having an optimal length path to u passing through link i. In the complete information case we show that a shortest path family uniquely determines the graph and conclude the existence of graphs such that any full information shortest path routing scheme requires a total of \Omega\Gamma n 2 ) memory bits. We also study the class of "unique shortest path graphs", i.e. graphs for which all vertices are connected by a unique shortest path. 1980 Mathematics Subject Classification: 6...
A Simple DFSBased Algorithm for Linear Interval Routing
 In Proc. th Int. Workshop on Distributed Algorithms
, 1997
"... . Linear Interval Routing is a spaceefficient routing method for pointtopoint communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wraparound. It was noted in [BLT91] that not every network ..."
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Cited by 1 (0 self)
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. Linear Interval Routing is a spaceefficient routing method for pointtopoint communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wraparound. It was noted in [BLT91] that not every network has a valid Linear Interval Labeling Scheme (LILS). A complete characterization of the networks that admit a valid LILS was presented in [FG94], together with an algorithm that generates a valid LILS in case one exists. We present a new algorithm that generates an LILS for every network that admits one. Our algorithm is based on a DFS spanning tree of the network, and is "in the spirit" of the algorithms for Interval Routing. Our algorithm has few advantages over the algorithm of [FG94]: it utilizes the wellknown theory of DFS spanning trees and is thus simpler to understand and to implement, it uses all links of the network for routing (thus it better distributes the load), and it guarant...