An Algorithm for Finding Two Node-Disjoint Paths in Arbitrary Graphs

Given two distinct vertices (nodes) source s and target t of a graph G = (V, E), the two node-disjoint paths problem is to identify two node-disjoint paths between s ∈ V and t ∈ V. Two paths are node-disjoint if they have no common intermediate vertices. In this paper, we present an algorithm with O(m)-time complexity for finding two node-disjoint paths between s and t in arbitrary graphs where m is the number of edges. The proposed algorithm has a wide range of applications in ensuring reliability and security of sensor, mobile and fixed communication networks

Survivable paths in multilayer networks

We consider the problem of protection in multilayer networks. In single-layer networks, a pair of disjoint paths can be used to provide protection for a source-destination pair. However, this approach cannot be directly applied to layered networks where disjoint paths may not always exist. In this paper, we take a new approach which is based on finding a set of paths that may not be disjoint but together will survive any single physical link failure. We consider the problem of finding the minimum number of survivable paths. In particular, we focus on two versions of this problem: one where the length of a path is restricted, and the other where the number of paths sharing a fiber is restricted. We prove that in general, finding the minimum survivable path set is NP-hard, whereas both of the restricted versions of the problem can be solved in polynomial time. We formulate the problems as Integer Linear Programs (ILPs), and use these formulations to develop heuristics and approximation algorithms.National Science Foundation (U.S.) (NSF grant CNS-0830961)National Science Foundation (U.S.) (NSF grant CNS-1017800)United States. Defense Threat Reduction Agency (grant HDTRA-09-1-005)United States. Defense Threat Reduction Agency (grant HDTRA1-07-1-0004

Finding Disjoint Paths on Edge-Colored Graphs: More Tractability Results

The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph (called MaxCDP) has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate how the complexity of the problem depends on graph parameters (namely the number of vertices to remove to make the graph a collection of disjoint paths and the size of the vertex cover of the graph), which makes sense since graphs in social networks are not random and have structure. The problem was known to be hard to approximate in polynomial time and not fixed-parameter tractable (FPT) for the natural parameter. Here, we show that it is still hard to approximate, even in FPT-time. Finally, we introduce a new variant of the problem, called MaxCDDP, whose goal is to find the maximum number of vertex-disjoint and color-disjoint uni-color paths. We extend some of the results of MaxCDP to this new variant, and we prove that unlike MaxCDP, MaxCDDP is already hard on graphs at distance two from disjoint paths.Comment: Journal version in JOC

Evaluation MCDM Multi-disjoint Paths Selection Algorithms Using Fuzzy-Copeland Ranking Method

To increase the Internet's reliability and to have greater control over traffic transmission, reliable path selection is important and Multipath routing is promising technique that are used in the communication networks. Finding reliable end-end paths and backup can increase network performance. So, using proper decision metrics and algorithm should be used to paths and backup selection phase in these networks. For this goal, in this paper selecting a more reliable multi disjoint paths is addressed as a multi-criteria decision making (MCDM) problem and availability factor is defined and calculated based on network histories. For decision algorithm, a new fuzzy evaluation method is proposed to rank these multi disjoint paths selection algorithms and it is compared with bandwidth based, TOPSIS, FuzzyTOPSIS and AHP methods as candidate techniques to select more appropriate global disjoint paths in the IP/MPLS networks with packet loss, delay and availability parameters as decision making metrics. The proposed method combines fuzzy theory and Copeland method to evaluate the rank of each proposed method base on bandwidth, delay and new defined availability metric of selected end to end paths. Simulation results show that this method selects more reliable backup paths with better bandwidth in compared with others and can be used to path selection in IP/MPLS networks

An effective algorithm for obtaining the whole set of minimal cost pairs of disjoint paths with dual arc costs

In telecommunication networks design the problem of obtaining optimal (arc or node) disjoint paths, for increasing network reliability, is extremely important. The problem of calculating kc disjoint paths from s to t (two distinct nodes), in a network with kc different (arbitrary) costs on every arc such that the total cost of the paths is minimised, is NP-complete even for kc = 2. When kc = 2 these networks are usually designated as dual arc cost networks. In this paper we propose an exact algorithm for finding the whole set of arc-disjoint path pairs, with minimal cost in a network with dual arc costs. The correctness of the algorithm is based on a condition which guarantees that the optimal path pair cost has been obtained and on a proposition which guarantees that at the end of the algorithm all the optimal pairs have been obtained. The optimality condition is based on the calculation of upper and lower bounds on the optimal cost. Extensive experimentation is presented to show the effectiveness of the algorithm

Optimization of Free Space Optical Wireless Network for Cellular Backhauling

With densification of nodes in cellular networks, free space optic (FSO) connections are becoming an appealing low cost and high rate alternative to copper and fiber as the backhaul solution for wireless communication systems. To ensure a reliable cellular backhaul, provisions for redundant, disjoint paths between the nodes must be made in the design phase. This paper aims at finding a cost-effective solution to upgrade the cellular backhaul with pre-deployed optical fibers using FSO links and mirror components. Since the quality of the FSO links depends on several factors, such as transmission distance, power, and weather conditions, we adopt an elaborate formulation to calculate link reliability. We present a novel integer linear programming model to approach optimal FSO backhaul design, guaranteeing $K$-disjoint paths connecting each node pair. Next, we derive a column generation method to a path-oriented mathematical formulation. Applying the method in a sequential manner enables high computational scalability. We use realistic scenarios to demonstrate our approaches efficiently provide optimal or near-optimal solutions, and thereby allow for accurately dealing with the trade-off between cost and reliability

A new algorithm for calculating the most reliable pair of disjoint paths in a network, Journal of Telecommunications and Information Technology, 2006, nr 4

In various types telecommunication networks, namely mobile ad hoc networks, WDM networks and MPLS networks, there is the necessity of calculating disjoint paths for given node to node connections in order to increase the reliability of the services supported by these networks. This leads to the problem of calculating a pair of disjoint paths (or a set of disjoint paths) which optimises some measure of performance in those networks. In this paper we present an algorithm, designated as OptDP, for obtaining the most reliable pair of disjoint paths based on the loopless version of MPS, a very efficient k-shortest path algorithm, and on Dijkstra algorithm. Since to the best of our knowledge there is no other proposal of an algorithm capable of solving exactly the same problem we perform a comparison with the application to this problem of the DPSP algorithm which calculates a set of disjoint paths with high reliability. Also a comparison with a simplified version (designated as NopDP) of the proposed algorithm, which stops after a maximal number F of candidate pairs of paths have been found, is presented. The comparison also includes the percentage of cases in which both algorithms were not capable of finding the optimal pair

On shortest disjoint paths and Hamiltonian cycles in some interconnection networks

Parallel processors are classified into two classes: shared-memory multiprocessors and distributed- memory multiprocessors. In the shared-memory system, processors communicate through a common memory unit. However, in the distributed multiprocessor system, each processor has its own memory unit and the communications among the processors are performed through an interconnection network. Thus, the interconnection topology plays an important role in the performance of these parallel systems. Recently, some new classes of interconnection networks, referred as Gaussian and Eisenstein- Jacobi networks, have been introduced. In this dissertation, we study the problem of finding the shortest node disjoint paths in the Gaussian and the Eisenstein-Jacobi networks. Moreover, we also describe how to generate edge disjoint Hamiltonian cycles in Eisenstein- Jacobi and Generalized Hypercube networks. Node disjoint paths are paths between any given source and destination nodes such that the paths have no common nodes except the endpoints. Similarly, edge disjoint Hamiltonian cycles are cycles in a given graph where each node is visited once and returns to the starting node and every edge is in at most one cycle.Keywords: Hamiltonian cycles, Disjoint paths, Parallel computing, Interconnection networ

Survivable paths in multilayer networks

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 75-77).We consider the problem of protection in multilayer networks. In single-layer net- works, a pair of disjoint paths can be used to provide protection for a source-destination pair. However, this approach cannot be directly applied to layered networks where disjoint paths may not always exist. In this thesis, we take a new approach which is based on finding a set of paths that may not be disjoint but together will survive any single physical link failure. First, we consider the problem of finding the minimum number of survivable paths. In particular, we focus on two versions of this problem: one where the length of a path is restricted, and the other where the number of paths sharing a fiber is restricted. We prove that in general, finding the minimum survivable path set is NP-hard, whereas both of the restricted versions of the problem can be solved in polynomial time. We formulate the problem as Integer Linear Programs (ILPs), and use these formulations to develop heuristics and approximation algorithms. Next, we consider the problem of finding a set of survivable paths that uses the minimum number of fibers. We show that this problem is NP-hard in general, and develop heuristics and approximation algorithms with provable approximation bounds. We also model the dependency of communication networks on the power grid as a layered network, and investigate the survivability of communication networks in this layered setting. Finally, we present simulation results comparing the different algorithms.by Marzieh Parandehgheibi.S.M