In this letter, we investigate the performance impact of disjoint multiple paths on SCTP in the connected MANET under emergency situations. Disjoint multiple paths allow multi-homing of SCTP to be fully utilized in MANETs, but it may cause inappropriate SACK handling. Through simulations, we evaluate the impact in terms of throughput and energy efficiency.

We propose a Multiple Zones-based (M-Zone) routing protocol to discover node-disjoint multiplath routing efficiently and effectively in large-scale MANETs. Compared with single path routing, multipath routing can improve robustness, load balancing and throughput of a network. However, it is very difficult to achieve node-disjoint multipath routing in large-scale MANETs. To ensure finding node-disjoint multiple paths, the M-Zone protocol divides the region between a source and a destination into multiple zones based on geographical location and each path is mapped to a distinct zone. Performance analysis shows that M-Zone has good stability, and the control complexity and storage complexity of M-Zone are lower than those of the well-known AODVM protocol. Simulation studies show that the average end-to-end delay of M-Zone is lower than that of AODVM and the routing overhead of M-Zone is less than that of AODVM.

Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.

In this paper we study the problem of how to identify multiple disjoint paths that have the minimum total cost OPT and satisfy a delay bound D in a graph G. This problem has lots of applications in networking such as fault-tolerant quality of service (QoS) routing and network-flow load balancing. Recently, several approximation algorithms have been developed for this problem. Here, we propose a new approximation algorithm for it by using the Lagrangian Relaxation method. We then present a simple approximation algorithm for finding multiple link-disjoint paths that satisfy the delay constraints at a reasonable total cost. If the optimal solution under delay-bound D has a cost OPT, then our algorithm can find a solution whose delay is bounded by (1+)D and the cost is no more than (1+k)OPT. The time complexity of our algorithm is much better than the previous algorithms.

In this paper, we propose an algorithm that solves the node-to-node disjoint paths problem in n-burnt pancake graphs in polynomial-order time of n. We also give a proof of its correctness as well as the estimates of time complexity O(n3) and the maximum path length 3n+4. We conducted a computer experiment for n=2 to 100 to measure the average performance of our algorithm. The results show that the average time complexity is O(n3.0) and the maximum path length is 3n+4.

In this paper, we give an algorithm for the node-to-set disjoint paths problem in a transposition graph. The algorithm is of polynomial order of n for an n-transposition graph. It is based on recursion and divided into two cases according to the distribution of destination nodes. The maximum length of each path and the time complexity of the algorithm are estimated theoretically to be O(n7) and 3n - 5, respectively, and the average performance is evaluated based on computer experiments.

An algorithm is described for solving the node-to-set disjoint paths problem in bi-rotator graphs, which are obtained by making each edge of a rotator graph bi-directional. The algorithm is of polynomial order of n for an n-bi-rotator graph. It is based on recursion and divided into three cases according to the distribution of destination nodes in the classes into which the nodes in a bi-rotator graph are categorized. We estimated that it obtains 2n-3 disjoint paths with a time complexity of O(n5), that the sum of the path lengths is O(n3), and that the length of the maximum path is O(n2). Computer experiment showed that the average execution time was O(n3.9) and, the average sum of the path lengths was O(n3.0).

A rotator graph was proposed as a topology for interconnection networks of parallel computers, and it is promising because of its small diameter and small degree. However, a rotator graph is a directed graph that sometimes behaves harmfully when it is applied to actual problems. A bi-rotator graph is obtained by making each edge of a rotator graph bi-directional. In a bi-rotator graph, average distance is improved against a rotator graph with the same number of nodes. In this paper, we give an algorithm for the container problem in bi-rotator graphs with its evaluation results. The solution achieves some fault tolerance such as file distribution based information dispersal technique. The algorithm is of polynomial order of n for an n-bi-rotator graph. It is based on recursion and divided into two cases according to the position of the destination node. The time complexity of the algorithm and the maximum length of paths obtained are estimated to be O(n3) and 4n-5, respectively. Average performance of the algorithm is also evaluated by computer experiments.

A burnt pancake graph is a variant of Cayley graphs and its topology is suitable for massively parallel systems. However, for a burnt pancake graph, there is much room for further research. Hence, in this study, we focus on n-burnt pancake graphs and propose an algorithm to obtain n disjoint paths from a source node to n destination nodes in polynomial order time of n, n being the degree of the graph. In addition, we estimate the time complexity of the algorithm and the sum of path lengths. We also give a proof of correctness of the algorithm. Moreover, we report the results of computer simulation to evaluate the average performance of the algorithm.

In this paper, we give an algorithm for the node-to-set disjoint paths problem in pancake graphs with its evaluation results. The algorithm is of polynomial order of n for an n-pancake graph. It is based on recursion and divided into two cases according to the distribution of destination nodes in classes into which all the nodes in a pancake graph are categorized. The sum of lengths of paths obtained and the time complexity of the algorithm are estimated and the average performance is evaluated based on computer simulation.

For any pair of distinct nodes in an n-pancake graph, we give an algorithm for construction of n-1 internally disjoint paths connecting the nodes in the time complexity of polynomial order of n. The length of each path obtained and the time complexity of the algorithm are estimated theoretically and verified by computer simulation.

In this paper, we give an algorithm for the node-to-set disjoint paths problem in rotator graphs with its evaluation results. The algorithm is based on recursion and it is divided into cases according to the distribution of destination nodes in classes into which all the nodes in a rotator graph are categorized. The sum of the length of paths obtained and the time complexity of the algorithm are estimated and verified by computer simulation.

In this paper we present a distributed routing protocol for finding two node-disjoint paths between each pair of nodes in a computer network. In the proposed protocol, each node in the network has the same procedure, which is driven by local information with respect to the network topology, such as adjacent nodes on a spanning tree in the network. Thus, the execution of the protocol can continue after changes of the network topology and load. Then, a spanning tree-based kernel construction is introduced to synchronize procedures under the distributed control of the protocol. Additionally, the routing scheme based on the protocol possesses the enhanced capabilities of alternate routes and load splitting, which cope with failures and load variations in the network. Thus, even if topology changes damage the obtained disjoint paths, the paths themselves can be updated efficiently.

In highly reliable communication network design, disjoint paths between pairs of nodes are often needed in the design phase. The problem of finding k paths which are as diverse as possible and have the lowest total cost is called a k-best paths problem. We propose an algorithm for finding the k-best paths connecting a pair of nodes in a graph G. Graph extension is used to transfer the k-best paths problem to a problem which deploits well-known maximum flow (MaxFlow) and minimum cost network flow (MCNF) algorithms. We prove the k-best paths solution of our algorithm to be an optimal one and the time complexity is the same as MCNF algorithm. Our computational experiences show that the proposed algorithm can solve k-best paths problem for a large network within reasonable computation time.

VP Network Designer, a software tool that automates the tasks involved in the transaction of service orders in VP leased line services, is introduced here in this paper. The tool is composed of two functions: VP Design Explorer which, given a request for VP establishment, determines a disjoint backup and target VP routes to support fault tolerance under VP-APS scheme; Network Resource Administrator which provides data administering functions, useful in maintaining a clear insight into the state of the network. The paper focuses on the implementation of VP Design Explorer. A scheme, proposed as disjoint VP routes search, is used to evaluate a pair of VP routes that guarantee duct level independence. The scheme is based on an integer programming modeling approach, and is proved to be effective for evaluating disjoint paths in a hierarchical network. VP Design Explorer is equipped with an additional feature where, under conditions of resource shortage, it presents a set of additional resources that are necessary to satisfy VP demand, together with the VP routes that become possible by the additions. Formulation of the problem is attained through an extension of the disjoint VP routes search scheme. A prototype of VP Network Designer is presented and its performance tested using computer simulations. The tool is found to achieve a computational time performance in the order of seconds and minutes, for evaluating disjoint VP routes search problems under real life ATM network conditions.

In this paper, we consider the following node-to-set disjoint paths problem: given a node s and a set T = {t1,...,tk} of k nodes in a k-connected graph G, find k node-disjoint paths s ti, 1 i k. We give an O(n2) time algorithm for the node-to-set disjoint paths problem in n-dimensional star graphs Gn which are (n - 1)-connected. The algorithm finds the n - 1 node-disjoint paths of length at most d(Gn) + 1 for n 4,6 and at most d(Gn) + 2 for n = 4,6, where d(Gn) = 3(n-1)/2 is the diameter of Gn. d(Gn) + 1 and d(Gn) + 2 are also the lower bounds on the length of the paths for the above problem in Gn for n 4,6 and n = 4,6, respectively.

In this paper, we study the following node-to-node and node-to-set routing problems in r-dimensional torus Trn with r 2 and n 4 nodes in each dimension: given at most 2r - 1 faulty nodes and non-faulty nodes s and t in Trn, find a fault-free path s t; and given at most 2r - k faulty nodes and non-faulty nodes s and t1,..., tk in Trn, find k fault-free node-disjoint paths s ti, 1 i k. We give an O(r2) time algorithm which finds a fault-free path s t of length at most d(Trn) + 1 for the node-to-node routing, where d(Trn) is the diameter of Trn. For node-to-set routing, we show an O(r3) time algorithm which finds k fault-free node-disjoint paths s ti, 1 i k, of length at most d(Trn) + 1. The upper bounds on the length of the found paths are optimal. From this, Rabin diameter of Trn is d(Trn) + 1.

In this paper, we give an algorithm which, given a set F of at most (n - 1) - k faulty nodes, and two sets S = {s1,..., sk} and T = {t1,..., tk}, 1 k n - 1, of nonfaulty nodes in n-dimensional star graphs Gn, finds k fault-free node disjoint paths si tji, where (j1,..., jk) is a permutation of (1,..., k), of length at most d(Gn) + 5 in O(kn) optimal time, where d(Gn) = 3(n-1)/2 is the diameter of Gn.

In this paper, we study the following node-to-node fault tolerant routing problem: In the presence of up to n-1 faulty nodes, find a fault-free path which connects any two non-faulty nodes s and t in an n-connected graph. For node-to-node fault tolerant routing in n-dimensional hypercubes Hn, we give an algorithm which finds a fault-free path s t of length at most in O(n) time, where d(s, t) is the distance between s and t. We also show that a fault-free path s t in Hn of length at most d(s, t)2i, 1i, can be found in time. For node-to-node fault tolerant routing in n-dimensional star graphs Gn, we give an algorithm which finds a fault-free path s t of length at most min{d(Gn)3, d(s, t)6} in O(n) time, where is the diameter of Gn. It is previously known that, in Hn, a fault-free path s t of length at most d(s, t) for d(s, t)n and at most d(s, t)2 for d(s, t)n can be found in O(d(s, t)n) time, and in Gn, a fault-free path s t of length at most min{d(Gn)1, d(s, t)4}can be found in O(d(s, t)n) time. When the time efficiency of finding the routing path is more important than the length of the path, the algorithms in this paper are better than the previous ones.

An optimal algorithm for decomposing a special type of the Hasse diagram into a minimum set of disjoint paths is described. It is useful for testing the consistency of functional dependencies.