Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints

For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\in Z^{+}$ and delay bound $D\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths subject to $C$ and $D$. This problem is known NP-hard, even when $k=1$ \cite{garey1979computers}. This paper first gives a simple approximation algorithm with factor-$(2,2)$, i.e. the algorithm computes a solution with delay and cost bounded by $2*D$ and $2*C$ respectively. Later, a novel improved approximation algorithm with ratio $(1+\beta,\,\max\{2,\,1+\ln\frac{1}{\beta}\})$ is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-$(1.369,\,2)$ approximation algorithm by setting $1+\ln\frac{1}{\beta}=2$ and a factor-$(1.567,\,1.567)$ algorithm by setting $1+\beta=1+\ln\frac{1}{\beta}$. Besides, by setting $\beta=0$, an approximation algorithm with ratio $(1,\, O(\ln n))$, i.e. an algorithm with only a single factor ratio $O(\ln n)$ on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the $k$BCP problem that strictly obeys the delay constraint.Comment: 12 page

Edge disjoint paths with minimum delay subject to reliability constraint

Recently, multipaths solutions have been proposed to improve the quality-of-service (QoS) in communication networks (CN). This paper describes a problem, DP/RD, to obtain the -edge-disjoint-path-set such that its reliability is at least R and its delay is minimal, for 1. DP/RD is useful for applications that require non-compromised reliability while demanding minimum delay. In this paper we propose an approximate algorithm based on the Lagrange-relaxation to solve the problem. Our solution produces DP that meets the reliability constraint R with delay(1+k)Dmin, for k1, and Dmin is the minimum path delay of any DP in the CN. Simulations on forty randomly generated CNs show that our polynomial time algorithm produced DP with delay and reliability comparable to those obtained using the exponential time brute-force approach

A New Approximation Algorithm for Computing 2-Restricted Disjoint Paths

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+1/k)D and the cost is no more than (1+k)OPT. The time complexity of our algorithm is much better than the previous algorithms. Copyright © 2007 The Institute of Electronics, Information and Communication Engineers

Some new localized quality of service models and algorithms for communication networks. The development and evaluation of new localized quality of service routing algorithms and path selection methods for both flat and hierarchical communication networks.

The Quality of Service (QoS) routing approach is gaining an increasing interest in the Internet community due to the new emerging Internet applications such as real-time multimedia applications. These applications require better levels of quality of services than those supported by best effort networks. Therefore providing such services is crucial to many real time and multimedia applications which have strict quality of service requirements regarding bandwidth and timeliness of delivery. QoS routing is a major component in any QoS architecture and thus has been studied extensively in the literature. Scalability is considered one of the major issues in designing efficient QoS routing algorithms due to the high cost of QoS routing both in terms of computational effort and communication overhead. Localized quality of service routing is a promising approach to overcome the scalability problem of the conventional quality of service routing approach. The localized quality of service approach eliminates the communication overhead because it does not need the global network state information. The main aim of this thesis is to contribute towards the localised routing area by proposing and developing some new models and algorithms. Toward this goal we make the following major contributions. First, a scalable and efficient QoS routing algorithm based on a localised approach to QoS routing has been developed and evaluated. Second, we have developed a path selection technique that can be used with existing localized QoS routing algorithms to enhance their scalability and performance. Third, a scalable and efficient hierarchical QoS routing algorithm based on a localised approach to QoS routing has been developed and evaluated