Partial characterizations of networks supporting shortest path interval labeling schemes

Narayanan, Lata; Shende, Sunil

doi:10.1002/(sici)1097-0037(199809)32:2<103::aid-net3>3.0.co;2-f

Cited by 10 publications

(12 citation statements)

References 6 publications

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“…Since every non-strict circular-arc graph G is an interval graph and therefore has strict compactness 1 [19], we only need to consider strict circular-arc graphs in the proof. For the rest of this section let (X, C ) be a clique-cycle for an arbitrary strict circular-arc graph G u = (V, E) and G = (V, A) be the directed symmetric version of G u .…”

Section: Resultsmentioning

confidence: 99%

Interval Routing Schemes for Circular-Arc Graphs

Gurski

Poullie

2017

Int. J. Found. Comput. Sci.

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Interval routing is a space efficient method to realize a distributed routing function. In this paper we show that every circular-arc graph allows a shortest path strict 2-interval routing scheme, i.e., by introducing a global order on the vertices and assigning at most two (strict) intervals in this order to the ends of every edge allows to depict a routing function that implies exclusively shortest paths. Since circular-arc graphs do not allow shortest path 1-interval routing schemes in general, the result implies that the class of circular-arc graphs has strict compactness 2, which was a hitherto open question. Additionally, we show that the constructed 2-interval routing scheme is a 1-interval routing scheme with at most one additional interval assigned at each vertex and we outline an algorithm to calculate the routing scheme for circular-arc graphs in O(n 2 ) time, where n is the number of vertices.

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Section: Resultsmentioning

confidence: 99%

Interval Routing Schemes for Circular-Arc Graphs

Gurski

Poullie

2017

Int. J. Found. Comput. Sci.

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“…There are many results on routing schemes for particular graph classes, including complete graphs, grids (alias meshes), hypercubes, complete bipartite graphs, unit interval and interval graphs, trees and 2-trees, rings, tori, unit circular-arc graphs, outerplanar graphs, and squaregraphs (see [1,9,13,14,21,25,30]). All those graph families admit routing schemes with O(d log n) labels and O(log d) routing decision (where d is the maximum degree of a vertex).…”

Section: Routing Labeling Schemesmentioning

confidence: 99%

Distance and routing labeling schemes for non-positively curved plane graphs

Chepoi¹,

Dragan²,

Vaxès³

2006

Journal of Algorithms

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Distance labeling schemes are schemes that label the vertices of a graph with short labels in such a way that the distance between any two vertices u and v can be determined efficiently (e.g., in constant or logarithmic time) by merely inspecting the labels of u and v, without using any other information. Similarly, routing labeling schemes are schemes that label the vertices of a graph with short labels in such a way that given the label of a source vertex and the label of a destination, it is possible to compute efficiently (e.g., in constant or logarithmic time) the port number of the edge from the source that heads in the direction of the destination. In this paper we show that the three major classes of nonpositively curved plane graphs enjoy such distance and routing labeling schemes using O(log 2 n) bit labels on n-vertex graphs. In constructing these labeling schemes interesting metric properties of those graphs are employed.

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“…However, at the present time, no characterization of 1-LIRS * and 1-IRS * is known. Recently, Narayanan and Shende have shown [22] that all interval graphs belong to 1-IRS * strict. We give below another class of graphs belonging to 1-IRS * strict.…”

Section: Definition 9 (Optimality) Let R Be a Routing Function On A mentioning

confidence: 99%

Interval Routing Schemes

Fraigniaud

Gavoille

1998

Algorithmica

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Interval routing was introduced to reduce the size of routing tables: a router finds the direction where to forward a message by determining which interval contains the destination address of the message, each interval being associated to one particular direction. This way of implementing a routing function is quite attractive but very little is known about the topological properties that must satisfy a network to support an interval routing function with particular constraints (shortest paths, limited number of intervals associated to each direction, etc.). In this paper we investigate the study of the interval routing functions. In particular, we characterize the set of networks which support a linear or a linear strict interval routing function with only one interval per direction. We also derive practical tools to measure the efficiency of an interval routing function (number of intervals, length of the paths, etc.), and we describe large classes of networks which support optimal (linear) interval routing functions. Finally, we derive the main properties satisfied by the popular networks used to interconnect processors in a distributed memory parallel computer.

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Partial characterizations of networks supporting shortest path interval labeling schemes

Cited by 10 publications

References 6 publications

Interval Routing Schemes for Circular-Arc Graphs

Interval Routing Schemes for Circular-Arc Graphs

Distance and routing labeling schemes for non-positively curved plane graphs

Interval Routing Schemes

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