Finding a disjoint path pair is an important component in survivable networks. Since the traffic is carried on the active (working) path most of the time, it is useful to find a disjoint path pair such that the length of the shorter path (to be used as the active path) is minimized. In this paper, we first address such a minmin problem. We prove that this problem is NP-complete in either single link cost (e.g. dedicated backup bandwidth) or dual link cost (e.g. shared backup bandwidth) networks. In addition, it is NP-hard to obtain a k-approximation to the optimal solution for any k>1. Our proof is extended to another open question regarding the computational complexity of a restricted version of the min-sum problem in an undirected network with ordered dual cost links (called MSOD problem). To solve the minmin problem efficiently, we introduce a novel concept called conflicting link set which provides insights into the so-called trap problem, and develop a divide-and-conquer strategy. The result is an effective heuristic for the minmin problem called COLE, which can outperform other approaches in terms of both the optimality and running time. We also apply COLE to the MSOD problem to efficiently provide shared path protection and conduct comprehensive performance evaluation as well as comparison of various schemes for shared path protection. We show that COLE not only processes connection requests much faster than existing ILP based approaches but also achieves a good balance among the AP length, bandwidth efficiency and recovery time.

Shared risk link group (SRLG) has been widely recognized as an important concept in survivable optical networks. The issues of avoiding the so-called "traps" in the path determination phase and maximizing bandwidth sharing are more challenging in providing shared SRLG protection than in providing shared path protection without considering SRLG. In this paper, we extend a algorithm for the scheme of protection with multiple segments (PROMISE) to provide efficient SRLG protection. The proposed algorithm uses a novel dynamic programming technology and achieves a higher bandwidth efficiency and lower request blocking probability.

Wavelength band switching (WBS) has only recently attracted attention from the optical networking industry for its practical importance in reducing the control complexity and cost of optical cross-connects (OXCs). However, WBS-related problems of theoretical interest have not been addressed thoroughly by the research community, and many issues are still wide open. In particular, WBS is different from wavelength routing, and thus techniques developed for wavelength-routed networks (including e.g., those for traffic grooming) cannot be directly applied to effectively address WBS-related problems. In this paper, we first propose a new multigranular OXC (MG-OXC) architecture for WBS, which is more flexible than any existing WBS node architectures. We also adopt the most powerful waveband assignment strategy, and develop an efficient heuristic algorithm called Balanced Path routing with Heavy-Traffic first (BPHT). To verify its near-optimality, we also develop an integer linear programming (ILP) model. Both the ILP and the BPHT algorithms can handle the case with multiple fibers per link and hence are more general than our previous single-fiber solutions X. Cao et al. (2002). We conduct a comprehensive evaluation of the benefits of WBS through detailed analysis and simulations. We show that the proposed heuristic BPHT can perform much better than a heuristic which applies the optimal routing and wavelength assignment (RWA) method. We also show that WBS using BPHT is even more beneficial in multifiber networks than in single-fiber networks in terms of reducing the port count. Our analytical and simulation results also provide valuable insights into the effect of wavelength band granularity, as well as the trade-offs between the wavelength-hop and the port count required in WBS networks.

Waveband switching (WBS) has attracted attention from the optical networking industry for its practical importance in reducing port count, the associated control complexity, and cost of optical cross-connects (OXCs). However, WBS-related problems of theoretical interest have not been addressed thoroughly by the research community and many issues are still wide open. In particular, WBS is different from wavelength routing and, thus, techniques developed for wavelength-routed networks (including for example, those for traffic grooming) cannot be directly applied to effectively address WBS-related problems. In this paper, we first develop an integer linear programming (ILP) model, which for a given set of lightpath requests, determines the routes and assigns wavelengths to the lightpaths so as to minimize the number of ports needed. Since the optimal WBS problem of minimizing the port count in WBS networks contains an instance of routing and wavelength assignment (RWA), which is NP-complete, we adopt a powerful waveband assignment strategy and develop an efficient heuristic algorithm called balanced path routing with heavy-traffic first waveband assignment (BPHT). Both the ILP and the heuristic algorithm can handle the case with multiple fibers per link. We conduct a comprehensive evaluation of the benefits of WBS through detailed analysis and simulations. For small networks, our results indicate that the performance of the BPHT heuristic is close to that achievable by using the ILP model and, hence verifying its near-optimality. We show that for larger networks, BPHT can perform better than its variation called balanced traffic routing with maximum-hop first waveband assignment and much better than another heuristic based on optimal (but waveband oblivious) RWA that minimizes wavelength resources. We also show that WBS using BPHT is even more beneficial in multifiber networks than in single-fiber networks in terms of reducing the port count. Our analytical and simulation results provide valuable insights into the effect of wavelength band granularity, as well as the tradeoffs between the wavelength-hop and the port count required in WBS networks.

The major challenges in designing survivable schemes are how to allocate a minimal amount of spare resources (e.g., bandwidth) using fast (e.g., polynomial-time) algorithms, and, in case a failure occurs, to be able to recover quickly from it. All existing approaches invariably make tradeoffs. We propose novel shared segment protection algorithms which make little or no compromise . We develop an elegant integer linear programming (ILP) model to determine an optimal set of segments to protect a given active path. Although the ILP approach is useful for a medium-size network, it is too time consuming for large networks. Accordingly, we also design a fast heuristic algorithm based on dynamic programming to obtain a near-optimal set of segments. Although the heuristic algorithm has a polynomial time complexity, it can achieve a bandwidth efficiency as high as some best-performing shared path protection schemes and, at the same time, much faster recovery than these shared path protection schemes. The proposed scheme is also applicable to a wide range of networking technologies, including Internet Protocol and wavelength-division multiplexing networks under the generalized multiprotocol label switched framework.

For pt.I see Chunming Qiao and Dahai Xu, INFOCOM'02, p.302-11, (2002). This paper describes a novel, ultra-fast heuristic algorithm to address an NP-hard optimization problem. One of its significances is that, for the first time, it is shown that a heuristic algorithm can also have better overall performance than its time-consuming, integer linear programming (ILP) based counterparts in the online case, which is non-intuitive. The proposed heuristic algorithm is useful for developing effective shared path (mesh) protection schemes that establish survivable connections in modern networks. The advantage of our heuristic algorithm over existing algorithms for finding a pair of link (or node) disjoint paths, active path (AP) and backup path (BP), comes from the following salient feature. It uses a so-called potential backup cost (PBC) function when selecting an AP in the first phase, in order to take into consideration the backup bandwidth needed by the corresponding BP yet to be chosen in the second phase. The PBC function is derived mathematically based on a rigorous statistical analysis of experimental data. While the use of PBC only requires partial aggregate information on existing connections and distributed control, it can also be applied even more effectively when complete information is available.