All-shortest-path 2-interval routing is NP-complete

2009 ◽  
Vol 32 (2) ◽  
pp. 479-489
Author(s):  
Kai Wang ◽  
Rui Wang ◽  
Yanyan Liu
Keyword(s):  
Shortest Path ◽  
Np Complete ◽  
Interval Routing

scholarly journals On the hardness of minimizing space for all-shortest-path interval routing schemes

2007 ◽  
Vol 389 (1-2) ◽  
pp. 250-264
Author(s):  
Rui Wang ◽  
Francis C.M. Lau ◽  
Yan Yan Liu
Keyword(s):  
Shortest Path ◽  
Routing Schemes ◽  
Interval Routing

On the Hardness of Devising Interval Routing Schemes

1997 ◽  
Vol 07 (01) ◽  
pp. 39-47 ◽  
Author(s):  
Michele Flammini
Keyword(s):  
Time Complexity ◽  
Compact Routing ◽  
Routing Schemes ◽  
Np Completeness ◽  
Routing Scheme ◽  
Np Complete ◽  
Interval Routing ◽  
General Networks

The k-Interval Routing Scheme (k-IRS) is a compact routing scheme on general networks. It has been studied extensively and recently been implemented on the latest generation of the INMOS transputer router chips. In this paper we investigate the time complexity of devising a minimal space k-IRS and we prove that the problem of deciding whether there exists a 2-IRS for any network G is NP-complete. This is the first hardness result for k-IRS where k is constant and the graph underlying the network is unweighted. Moreover, the NP-completeness holds also for linear and strict 2-IRS.

scholarly journals The complexity of shortest path and dilation bounded interval routing

2000 ◽  
Vol 234 (1-2) ◽  
pp. 85-107 ◽  
Author(s):  
Rastislav Kráľovič ◽  
Peter Ružička ◽  
Daniel Štefankovič
Keyword(s):  
Shortest Path ◽  
Bounded Interval ◽  
Interval Routing

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.

scholarly journals Minimum Eccentricity Shortest Path Problem with Respect to Structural Parameters

2021 ◽  
pp. 442-455
Author(s):  
Martin Kučera ◽  
Ondřej Suchý
Keyword(s):  
Shortest Path ◽  
Undirected Graph ◽  
Structural Parameters ◽  
Shortest Path Problem ◽  
Disjoint Paths ◽  
Leaf Number ◽  
Fpt Algorithms ◽  
Np Complete ◽  
Cluster Graph

AbstractThe Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity in a given undirected graph. The problem is known to be NP-complete and W[2]-hard with respect to the desired eccentricity. We present fpt algorithms for the problem parameterized by the modular width, distance to cluster graph, the combination of distance to disjoint paths with the desired eccentricity, and maximum leaf number.

An Improved QoS Routing Algorithm in Internet

2013 ◽  
Vol 443 ◽  
pp. 487-493
Author(s):  
Hong Bo Huang ◽  
Yong Zhi Wang
Keyword(s):  
Shortest Path ◽  
Routing Algorithm ◽  
Shortest Paths ◽  
Space Reduction ◽  
Link Weight ◽  
Look Ahead ◽  
Np Complete ◽  
Qos Routing Algorithm ◽  
Definition Of ◽  
State Space Reduction

An Efficient Routing Algorithm for Improving the QoS in Internet has been proposed and presented in this paper. The algorithm is a kind of Multi Constrained Path algorithm. The routing take place based on more than one link weight components. To avoid the NP complete problem and to increase the computational efficiency some advancement are added. These include the definition of Non Linear Path Length, where the sub paths may not be the shortest path, having k no of shortest paths in a node instead of having only the shortest path, then removing the path dominancy for state space reduction. As a last the concept look ahead is also included through which a predicted path to destination is mapped. This work only implements the removal of path dominancy where the queue is updated by removing the dominated paths from the queue. The simulation is also showing the better performance of the system.

scholarly journals Worst Case Bounds for Shortest Path Interval Routing

1998 ◽  
Vol 27 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Cyril Gavoille ◽  
Eric Guévremont
Keyword(s):  
Shortest Path ◽  
Worst Case ◽  
Interval Routing
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