scholarly journals An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications

Algorithmica ◽  
1995 ◽  
Vol 14 (5) ◽  
pp. 429-441 ◽  
Author(s):  
M. J. Atallah ◽  
D. Z. Chen ◽  
D. T. Lee
Keyword(s):  
Optimal Algorithm ◽  
Shortest Paths ◽  
Circular Arc ◽  
Circular Arc Graphs

scholarly journals Interval Routing Schemes for Circular-Arc Graphs

2017 ◽  
Vol 28 (01) ◽  
pp. 39-60
Author(s):  
Frank Gurski ◽  
Patrick Gwydion Poullie
Keyword(s):  
Shortest Path ◽  
Shortest Paths ◽  
Global Order ◽  
Circular Arc ◽  
Distributed Routing ◽  
Routing Schemes ◽  
Routing Scheme ◽  
Interval Routing ◽  
Circular Arc Graphs ◽  
Open Question

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(n2) time, where n is the number of vertices.

Surjective L (2, 1)-labeling of cycles and circular-arc graphs

2018 ◽  
Vol 35 (1) ◽  
pp. 739-748 ◽  
Author(s):  
Sk. Amanathulla ◽  
Madhumangal Pal
Keyword(s):  
Circular Arc ◽  
Circular Arc Graphs

An $O(n^2 )$ Algorithm for Coloring Proper Circular Arc Graphs

1981 ◽  
Vol 2 (2) ◽  
pp. 88-93 ◽  
Author(s):  
James B. Orlin ◽  
Maurizio A. Bonuccelli ◽  
Daniel P. Bovet
Keyword(s):  
Circular Arc ◽  
Circular Arc Graphs ◽  
Proper Circular Arc Graphs

scholarly journals Structural results on circular-arc graphs and circle graphs: A survey and the main open problems

2014 ◽  
Vol 164 ◽  
pp. 427-443 ◽  
Author(s):  
Guillermo Durán ◽  
Luciano N. Grippo ◽  
Martín D. Safe
Keyword(s):  
Open Problems ◽  
Circle Graphs ◽  
Circular Arc ◽  
Circular Arc Graphs
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