A Stabilizing Algorithm for Finding Two Node-Disjoint Paths in Arbitrary Networks

To achieve the goal of security and privacy in future mobile communication networks, further research and technology development will be required. The roadmap presented in this chapter pioneers the boundaries of mobile privacy and security from a broad perspective. It registers the mobile privacy and security requirements of the actors on whom the success of future mobile communications, systems and services depends, it gives an overview of the current state-of-the-art in mobile security and privacy, addresses non-technical aspects, conducts a SWOT analysis from a European perspective and ultimately identifies the areas where research, standardisation and development will be most needed and beneficial in the coming years, so that we can progress rapidly and efficiently towards a trusted mobile environment.

Optimal node-disjoint paths in folded hypercubes

Orthogonal graphs are natural extensions of the classical binary and b-ary hypercubes b=2/sup l/ and are abstractions of interconnection schemes used for conflict-free orthogonal memory access in multiprocessor design. Based on the type of connection mode, these graphs are classified into two categories: those with disjoint and those with nondisjoint sets of modes. The former class coincides with the class of b-ary b=2/sup l/ hypercubes, and the latter denotes a new class of interconnection. It is shown that orthogonal graphs are Cayley graphs, a certain subgroup of the symmetric (permutation) group. Consequently these graphs are vertex symmetric, but it turns out that they are not edge symmetric. For an interesting subclass of orthogonal graphs with minimally nondisjoint set of modes, the shortest path routing algorithm and an enumeration of node disjoint (parallel) paths are provided. It is shown that while the number of node disjoint paths is equal to the degree, the distribution is not uniform with respect to Hamming distance as in the binary hypercube.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We consider the Maximum Node Disjoint Paths (MNDP) problem in undirected graphs. The input consists of an undirected graph G = (V, E) and a collection {(s1, t1), …, (sk, tk)} of k source-sink pairs. The goal is to select a maximum cardinality subset of pairs that can be routed/connected via node-disjoint paths. A relaxed version of MNDP allows up to c paths to use a node, where c is the congestion parameter. We give a polynomial time algorithm that routes Ω(OPT/poly log k) pairs with O(1) congestion, where OPT is the value of an optimum fractional solution to a natural multicommodity flow relaxation. Our result builds on the recent breakthrough of Chuzhoy [17] who gave the first poly-logarithmic approximation with constant congestion for the Maximum Edge Disjoint Paths (MEDP) problem.

Several real-time applications (e.g., video conferencing, remote control systems) demand guarantees on the message delivery latency. Supporting these QoS connections requires the existence of a routing mechanism, which computes paths that satisfy QoS delay constraints (e.g., end-to-end delays or failure recovery delays). In mobile ad hoc network, wireless links tend to frequently fail as nodes move in and out of transmission range of one another. Providing fault tolerance with QoS guarantees in such a network is challenging. The proposed new algorithm, also called a segmented backup routing (SBR), constructs a set of segmented backup paths. Each segmented backup path, protects a segment of the primary path rather than the entire path. The most important points that are made in this algorithm are two. First, one is able to identify backup paths for any selected primary path, as long as there exists a pair of node disjoint paths from source to destination. In other words, if there are two node disjoint paths, one is not forced to use either of them to be the primary path. This has the advantage that the primary path may be selected based on QoS considerations rather than a consideration of fault tolerance. The second advantage is that there are multiple backup paths, each of which protects breakdown of one or more nodes on the primary path. A backup path may be selected based on QoS considerations. In this paper, we have primarily focused on end-to-end delay as the QoS parameter. We apply our scheme to the AODV protocol.

Star networks were proposed recently as an attractive alternative to the well-known hypercube models for interconnection networks. Extensive research has been performed that shows that star networks are as versatile as hypercubes. This paper is an effort in the same direction. Based on the well-known paradigms, we study the one-to-many parallel routing problem on star networks and develop an improved routing algorithm that finds n-1 node-disjoint paths between one node and a set of other n-1 nodes in the n-star network. These parallel paths are proven of minimum length within a small additive constant, and the running time of our algorithm is bounded by O(n/sup 2/). More specifically, given a node s and n-1 other nodes {t/sub 1/, t/sub 2/, ..., t/sub n-1/} in the n-star network, our algorithm constructs n-1 node-disjoint paths P/sub 1/, P/sub 2/, ..., P/sub n-1/, where P/sub i/ is a path from s to t/sub j/ of length at most dist(s, t/sub j/)+6 and dist(s, t/sub j/) is the distance, i.e., the length of a shortest path, from s to t/sub j/, for i=1, 2, ..., n-1.The best bound on the path length by previously known algorithms for the same problem is 5(n-2)/spl ap/10/spl Delta//sub n//3, where /spl Delta//sub n/=max{dist(s, t)} is the diameter of the n-star network.

Chapter 18 - Evolution of TETRA through the integration with a number of communication platforms to support public protection and disaster relief (PPDR)

The reliability of a probabilistic communication network is considered. A probabilistic communication network is a network in which each branch is given a probability that the specific branch can perform its purpose successfully. This probability is called the reliability of this branch. The idea of the overall reliability of the simultaneous communication among all (or part of) the stations of a given network is introduced, rather than the pairwise reliability between any two stations as was discussed in previous works along this line. The overall reliability of a communication network is defined as the probability that simultaneous communication can be secured among all the stations; two formulas are given to enumerate it in terms of the branch reliabilities. An approximation is developed to calculate the overall reliability through the incidence matrix of the network when all the branch reliabilities are very small. Also, a criterion to compare relative importance of the roles played by all the branches is established by defining a quantity load for each branch. Two efficient algorithms are derived to find a most reliable subnetwork with no redundant branches. In addition, an exhausting method is furnished for the case of seeking simultaneous communication among only part of the terminals of the network.

We consider routing in survivable networks that provide protection against node or link failures. In these networks resilience against failures is provided by routing connections on pairs of disjoint paths called primary and backup paths. The primary path of a connection carries its traffic under normal circumstances and in the eventuality of a network failure effecting the primary path the connection traffic (all or some portion of it) is rerouted over its backup path. In an online setting as connection requests arrive a pair of disjoint primary and backup paths of least total cost (under some link cost metric) are selected to route the connections. In many situations the cost metric used for the primary path differs from the cost metric used for the backup path. Also in many realistic settings these two cost metrics are related to each other. In this paper we study the problem of finding a pair of edge or node disjoint paths of least total cost where the cost of the primary path is the total cost of its links while the cost for the backup path is α times the sum of the cost of its links, for some given α < 1. We show that the problem is hard to approximate to within a factor $$\Omega((\frac{1}{\alpha})^{1-\epsilon})$$ for any positive $$\epsilon \le 1$$ . In addition we show that the problem is complete for a set of hard to approximate problems. On the positive side we show that a simple algorithm achieves an approximation ratio of $$O(\frac{1}{\alpha})$$ for the problem.

Multipath routing plays an important role in communication networks. It can increase the effective bandwidth between pairs of vertices, avoid congestion in a network and reduce the probability of dropped packets. In this paper, we built model for vertex-disjoint paths problem and then proposed algorithm for finding the shortest pair of vertex-disjoint paths. We consider in this paper the shortest-path problem in networks in which the length (or weight) of the edges are considered. We present algorithms for finding the shortest-path. In more restricted transit. Furthermore, we can extend this algorithm to find any k disjoint paths whose sum-weight is minimized.

A survey on the communication architectures in smart grid

The existence of parallel node-disjoint paths between any pair of nodes is a desirable property of interconnection networks, because such paths allow tolerance to node and/or link failures along some of the paths, without causing disconnection. Additionally, node-disjoint paths support high-throughput communication via the concurrent transmission of parts of a message. We characterize maximum-sized families of parallel paths between any two nodes of alternating group networks. More specifically, we establish that in a given alternating group network AN n , there exist n?1 parallel paths (the maximum possible, given the node degree of n?1) between any pair of nodes. Furthermore, we demonstrate that these parallel paths are optimal or near-optimal, in the sense of their lengths exceeding the internode distance by no more than four. We also show that the wide diameter of AN n is at most one unit greater than the known lower bound D+1, where D is the network diameter.

Multipath and disjoint path routing schemes have received a considerable amount of attention in the networking research community in recent years due to many of advantages offered by such schemes. Delay, delay-jitter, bandwidth, are often used as parameters to specify quality-of-service. One of the most important parameters is the bandwidth of the route used for data transmission. A path from a source node s to a destination node t is known as the widest path if the bandwidth of this path is the largest among all paths between s to t. Algorithms for computing a widest path between a source-destination node pair is well-known. In this paper, we consider two problems where the notions of multipath, disjoint path and widest path are combined. In one version, we address the problem of finding a pair of disjoint paths between a source-destination node pair, such that the combined bandwidth of this path-pair is the maximum over all such pairs. In the other version, we want to find a pair of disjoint paths, such that the bandwidth of the first path is at least X/sub 1/ and the bandwidth of the second path is at least X/sub 2/, for some pre-specified values X/sub 1/ and X/sub 2/. We prove that both versions of the problem are NP-complete. We provide exact and approximate solutions for both versions of the problem. We show that our approximate solutions provide near-optimal solutions for almost all the instances of the problem.

Linear time distributed construction of colored trees for disjoint multipath routing

With the convergence of mobile and fixed communication networks, mobile users are increasingly demanding applications offering the same quality of service (QoS) as provided by wired access. High-speed time division duplex access mode is typical of high-speed mobile communication systems in order to simultaneously handle real-time, interactive, and best effort traffic classes. This paper proposes a medium access control (MAC) protocol that makes efficient use of radio resources for access. The proposed protocol, named dynamic-time division duplexing (D-TDD), is based on a multiple-access TDD air interface capable of supporting uplink and downlink traffic asymmetries. Validation of the D-TDD good performance was achieved by comparison with an ideal scheme and a different MAC protocol recently proposed in the literature on this subject.