Turgay Korkmaz

Multi-constrained optimal path selection

Providing quality-of-service (QoS) guarantees in packet networks gives rise to several challenging issues. One of them is how to determine a feasible path that satisfies a set of constraints while maintaining high utilization of network resources. The latter objective implies the need to impose an additional optimality requirement on the feasibility problem. This can be done through a primary cost function (e.g., administrative weight, hop count) according to which the selected feasible path is optimal. In general, multi-constrained path selection, with or without optimization, is an NP-complete problem that cannot be exactly solved in polynomial-time. Heuristics and approximation algorithms with polynomial and pseudo-polynomial-time complexities are often used to deal with this problem. However, existing solutions suffer either from excessive computational complexities that cannot be used for online network operation or from low performance. Moreover, they only deal with special cases of the problem (e.g., two constraints without optimization, one constraint with optimization, etc.). For the feasibility problem under multiple constraints, some researchers have proposed a nonlinear cost function whose minimization provides a continuous spectrum of solutions ranging from a generalized linear approximation (GLA) to an asymptotically exact solution. We propose an efficient heuristic algorithm for the most general form of the problem. We first formalize the theoretical properties of the above nonlinear cost function. We then introduce our heuristic algorithm (H MCOP), which attempts to minimize both the nonlinear cost function (for the feasibility part) and the primary cost function (for the optimality part). We prove that H MCOP guarantees at least the performance of GLA and often improves upon it. H MCOP has the same order of complexity as Dijkstras algorithm. Using extensive simulations on random graphs with correlated and uncorrelated link weights, we show that under the same level of computational complexity, H MCOP outperforms its (less general) contenders in its success rate in finding feasible paths and in the cost of such paths.

An overview of constraint-based path selection algorithms for QoS routing

Constraint-based path selection aims at identifying a path that satisfies a set of quality of service (QoS) constraints. In general, this problem is known to be NP-complete, leading to the proposal of many heuristic algorithms. We provide an overview of these algorithms, focusing on restricted shortest path and multi-constrained path algorithms.

Source-oriented topology aggregation with multiple QoS parameters in hierarchical networks

In this paper, we investigate the problem of topology aggregation (TA) for scalable, QoS-based routing in hierarchical networks. TA is the process of summarizing the topological information of a subset of network elements. This summary is flooded throughout the network and used by various nodes to determine appropriate routes for connection requests. A key issue in the design of a TA scheme is the appropriate balance between compaction and the corresponding routing performance. The contributions of this paper are twofold. First, we introduce a source-oriented approach to TA, hich provides better performance than existing approaches. The intuition behind this approach is that the advertised topology-state information is used by source nodes to determine tentative routes for connection requests. Accordingly, only information relevant to source nodes needs to be advertised. We integrate the source-oriented approach into three new TA schemes that provide different trade-offs between compaction and accuracy. Second, we extend our source-oriented approach to multi-QoS-based TA. A key issue here is the determination of appropriate values for the multiple QoS parameters associated with a logical link. Two new approaches to computing these values are introduced. Extensive simulations are used to evaluate the performance of out proposed schemes.

Bandwidth-delay constrained path selection under inaccurate state information

One of the key issues in any quality-of-service (QoS) routing framework is how to compute a path that satisfies given QoS constraints. In this paper, we focus on the path computation problem subject to the bandwidth and delay constraints. This problem can be easily solved if the exact state information is available to the node performing the path computation function. In practice, however, nodes have only imprecise knowledge of the network state. The reliance on outdated information and treating this information as exact can significantly degrade the effectiveness of the path selection algorithm. To address this problem, we adopt a probabilistic approach in which the state parameters (available bandwidth and delay) are characterized by random variables. The goal is then to find the most-probable bandwidth-delay-constrained path (MP-BDCP). We provide efficient solutions for the MP-BDCP problem by decomposing it into two subproblems: the most-probable delay-constrained path (MP-DCP) problem and the most-probable bandwidth-constrained path (MP-BCP) problem. MP-DCP by itself is known to be NP-hard, necessitating the use of approximate solutions. By employing the central limit theorem and Lagrange relaxation techniques, we provide two complementary solutions for MP-DCP. These solutions are found to be highly efficient, requiring on average a few iterations of Dijkstras shortest path algorithm. As for MP-BCP, it can be easily transformed into a variant of the shortest path problem. Our solutions for MP-DCP and MP-BCP are then combined to address the MP-BDCP problem by obtaining a set of near-nondominated paths. Decision makers can then select one or more of these paths based on a specific utility function. Extensive simulations are used to demonstrate the efficiency of the proposed algorithmic solutions and, more generally, to contrast the probabilistic path selection approach with the standard threshold-based triggered approach.

Performance evaluation of constraint-based path selection algorithms

Constraint-based path selection is an invaluable part of a full-fledged quality of service (QoS) architecture. Internet service providers want to be able to select paths for QoS flows that optimize network utilization and satisfy user requirements and as such increase revenues. Unfortunately, finding a path subject to multiple constraints is known to be an NP-complete problem. Hence, accurate constraint-based path selection algorithms with a fast running time are scarce. Numerous heuristics and a few exact algorithms have been proposed. In this article we compare most of these algorithms. We focus on the restricted shortest path algorithms and multi-constrained path algorithms. The performance evaluation of these two classes of algorithms is presented based on complexity analysis and simulation results and may shed some light on the difficult task of selecting the proper algorithm for a QoS-capable network.

Quality of Service Routing

Constraint-based routing is an invaluable part of a full- fledged Quality of Service architecture. Unfortunately, QoS routing with multiple additive constraints is known to be a NP-complete problem. Hence, accurate constraint-based routing algorithms with a fast running time are scarce, perhaps even non-existent. The need for such algorithms has resulted in the proposal of numerous heuristics and a few exact solutions.

A randomized algorithm for finding a path subject to multiple QoS requirements

Abstract An important aspect of quality-of-service (QoS) provisioning in integrated networks is the ability to find a feasible route that satisfies a set of end-to-end QoS requirements (or constraints) while efficiently using network resources. In general, finding a path subject to multiple additive constraints (e.g., delay, delay-jitter) is an NP-complete problem. We propose an efficient randomized heuristic algorithm to this problem. Although the algorithm is presented as a centralized one, the idea behind it can also be implemented in a distributed manner. Our algorithm initially computes the cost of the best path from each node to a given destination with respect to individual link weights and their linear combination. In this initialization step, Reverse–Dijkstras algorithm is used K +1 times per path request, where K is the number of additive constraints. The algorithm then randomly traverses the graph, discovering nodes from which there is a good chance of reaching the final destination. This randomized search is a modification of the breadth-first search (BFS). Using extensive simulations, we show that the proposed algorithm provides better performance than existing algorithms under the same order of computational complexity.

Single packet IP traceback in AS-level partial deployment scenario

Denial-of-Service (DoS) attacks commonly use IP spoofing to hide the identity and the location of the attack origin. To defend against various DoS attacks and make the attacker accountable, it is necessary to trace IP packets regardless of their source addresses. In this direction, log-based IP traceback is a promising and powerful approach due to its ability to traceback even a single packet. However, the global deployment of log-based IP traceback at all the routers in the internet requires a significant amount of modifications in the routers and introduces a serious operation and management overhead. To facilitate global deployment, we consider the Autonomous Systems (AS) level deployment of log-based IP traceback and accordingly propose a new mechanism called AS-level Single Packet Traceback (AS-SPT). We then evaluate the performance and overhead of the proposed AS-SPT under various partial deployment scenarios.

Routing multimedia traffic with QoS guarantees

One of the challenging issues in exchanging multimedia information over a network is how to determine a feasible path that satisfies all the quality-of-service (QoS) requirements of multimedia applications while maintaining high utilization of network resources. The latter objective implies the need to impose an additional optimality requirement on the feasibility problem. This can be done through a primary cost function (e.g., administrative weight, hop-count) according to which the selected feasible path is optimal. In general, multiconstrained path selection, with or without optimization, is an NP-complete problem that cannot be exactly solved in polynomial time. Heuristics and approximation algorithms with polynomial- and pseudo-polynomial-time complexities are often used to deal with this problem. However, existing solutions suffer either from excessive computational complexities that cannot be used for online network operation or from low performance. Moreover, they only deal with special cases of the problem (e.g., two constraints without optimization, one constraint with optimization, etc.). For the feasibility problem under multiple constraints, some researchers have recently proposed a nonlinear cost function whose minimization provides a continuous spectrum of solutions ranging from a generalized linear approximation (GLA) to an asymptotically exact solution. In this paper, we propose an efficient heuristic algorithm for the most general form of the problem. We first formalize the theoretical properties of the above nonlinear cost function. We then introduce our heuristic algorithm (H/spl I.bar/MCOP), which attempts to minimize both the nonlinear cost function (for the feasibility part) and the primary cost function (for the optimality part). We prove that H/spl I.bar/MCOP guarantees at least the performance of GLA and often improves upon it. H/spl I.bar/MCOP has the same order of complexity as Dijkstras algorithm. Using extensive simulations on random graphs and realistic network topologies with correlated and uncorrelated link weights from several distributions including uniform, normal, and exponential, we show the efficiency of H/spl I.bar/MCOP over its (less general) contenders in terms of finding feasible paths and minimizing their costs under the same level of computational complexity.

An efficient algorithm for finding a path subject to two additive constraints

One of the key issues in providing end-to-end quality-of-service (QoS) guarantees in packet networks is how to determine a feasible path that satisfies a number of QoS constraints. For two or more additive constraints, the problem of finding a feasible path is NP-complete that cannot be exactly solved in polynomial time. Accordingly, several heuristics and approximation algorithms have been proposed for this problem. Many of these algorithms suffer from either excessive computational cost or low performance. In this paper, we provide an efficient approximation algorithm for finding a path subject to two additive constraints. The worst-case computational complexity of this algorithm is within a logarithmic number of calls to Dijkstras shortest path algorithm. Its average complexity is even much lower than that, as demonstrated by simulation experiments. The performance of the proposed algorithm is justified via theoretical bounds that are provided for the optimal version of the path selection problem. To achieve further performance improvement, several extensions to the basic algorithm are also provided at very low computational cost. Extensive simulations are used to demonstrate the high performance of the proposed algorithm and to contrast it with other path selection algorithms.