Link-disjoint Paths Research Articles

Minimum-Weight Link-Disjoint Paths With a Bounded Number of Shared Nodes

Network protection has drawn a certain interest in network optimization. One of the most effective and widely used methods to protect networks from failures is to establish backup paths for working paths. For example, we find k node-disjoint paths between a source and a sink with one working path and k-1 backup paths. However, the demand for full protection of a network is somewhat too restrictive and there may not exist k node-disjoint paths in the network due to the limitation of geographical environments. On the other hand, the occurrence probability of node failures is usually much less than that of link failures in real-world models. To save network resources, we turn to establish link-disjoint paths allowing a few shared nodes. We study the problem of finding k link-disjoint paths between a source and a sink under the constraint that the number of nodes shared by at least r paths is at most δ, minimizing the total link weight. First, we systematically study the computational complexity of the problem with respect to three parameters k, r, and δ. Then, we build an integer linear programming for the general model and design a polynomial-time algorithm for the case that k=r by using the techniques of augmenting paths and splitting nodes. Finally, we carry out experimentations on synthetic and real networks that show the effectiveness of our algorithms in practice.

Reliable Provisioning With Degraded Service Using Multipath Routing From Multiple Data Centers in Optical Metro Networks

With the adoption of edge computing, several data centers are available within the footprint of an optical metro network, and contents are replicated in multiple locations. Such a wide content replication offers a unique opportunity to provide better services to users, especially for content-based services, e.g., video delivery. Thus, a service-provisioning scheme can embrace this opportunity to optimize network resource utilization, improve reliability, and achieve lower latency. In this study, we propose a reliable service-provisioning scheme that selects the optimal subset of data centers hosting the desired content and inversely multiplexes a content request over multiple link-disjoint paths. We formulate an integer linear program and develop heuristics for the problem, and use them to solve various complex and realistic network instances. Numerical data show that, compared to conventional service-provisioning schemes such as multipath routing from a single data center or dedicated-path protection, our proposed scheme efficiently utilizes network resources, improves reliability, and reduces latency; hence, it is suitable for the above-mentioned services.

Green Multistage Upgrade of Switches and Controllers for Bundled-Links SDNs

The switches in legacy networks perform both control and data forwarding operations. In contrast, in a software defined network (SDN), a controller is responsible for network control and each SDN-switch (<i>s</i>-switch) only forwards data packets. Advantageously, controllers can be upgraded easily to run state-of-the-art network configuration and management solutions. In this context, this paper addresses the novel problem of upgrading a legacy network into an SDN over multiple stages that span months or years. More specifically, it aims to minimize energy consumption by optimizing switch upgrades, controller placement, and traffic routing subject to an operator&#x2019;s budget, traffic delay tolerance, and controller capacity. We formulate the problem as a mixed integer program (MIP), and develop a heuristic solution that ensures a single path is used between switches and up to two link-disjoint paths are used between an s-switch and its controller. Our simulation results show that increasing an operator&#x2019;s budget and the number of upgrade stages reduce the energy consumption of tested networks by 68.42%. Further, our heuristic solution yields energy saving that is within 5% away from the optimal value. In addition, deploying controllers at strategic locations saves more energy than placing them at arbitrary locations. Lastly, our heuristic solution guarantees the delay requirement of traffic demands and runs up to 307 times faster than a prior solution.

Multi-path provisioning in elastic optical network with dynamic on-request optimal defragmentation strategy

Elastic Optical Networks (EONs) are extensively accepted promising solution for future ultra-high-speed optical transmission, due to their capability of efficient and flexible assignment of immense optical bandwidth to the heterogeneous traffic demand. However, it undergoes through an aggravated form of the spectrum fragmentation problem due to the heterogeneous bandwidth requirements, spectrum continuity and contiguity constraints. Several techniques have been presented in the literature to get the optimal solution of this problem while multi-path provisioning comes out to be very compelling among them. Although, it creates further challenges due to high hardware requirement and more spectrum consumption due to guard-bands. In this paper, we propose a novel scheme, called optimal spectrum defragmentation (DF) strategy with split spectrum approach (OSDSSA), to tackle this limitation of multi-path provisioning by utilizing minimum number of spectral paths, which improves the scalability, reduces the extra spectrum consumption by guard-bands and avoids the exhaustion of transponders at nodes. The proposed scheme initially serves a connection request using k-shortest routing paths and first-fit spectrum allocation policy in a best possible way. In case, if a connection request cannot be served then the proposed mechanism proceeds with the triggering of Process Defragmentation on the link disjoint shortest paths followed by splitting of traffic demand on corresponding link-disjoint paths. The Process Defragmentation is triggered on the active connections at the immediate right and left of the largest continuous available spectrum block on the link-disjoint shortest paths sequentially until the requested amount of frequency slots (FSs) are achieved. In this work, reconfiguration includes spectrum re-tuning without changing the routing paths, thereby reducing the unnecessary service disruption, DF complexity and cost, leading to improvement in quality of service (QoS) of the network. The performance of the proposed scheme has been assessed through simulation results where single path and multi-path provisioning algorithms have been considered as benchmarks. Through our proposed scheme bandwidth blocking performance, spectrum utilization ratio, and degree of fragmentation have also been improved significantly.

Finding Minimum-Weight Link-Disjoint Paths with a Few Common Nodes

Network survivability has drawn certain interest in network optimization. However, the demand for full protection of a network is usually too restrictive. To overcome the limitation of geographical environments and to save network resources, we turn to establish backup networks allowing a few common nodes. It comes out the problem of finding k link-disjoint paths between a given pair of source and sink in a network such that the number of common nodes shared by at least two paths is bounded by a constant and the total link weight of all paths is minimized under the above constraints. For the case k = 2, where we have only one backup path, several fast algorithms have been developed in the literature. For the case k &gt; 2, little results are known. In this paper, we first establish the NP-hardness of the problem with general k. Motivated by the situation that each node in a network may have a capability of multicasting, we also study a restricted version with one more requirement that each node can be shared by at most two paths. For the restricted version, we build an ILP model and design a fast algorithm by using the techniques of augmenting paths and splitting nodes. Furthermore, experimental results on synthetic and real networks show that our algorithm is effective in practice.

An Asynchronous Distributed Algorithm for Minimum [formula omitted] Cut Detection in Wireless Multi-hop Networks

Stable communication is a vital and challenging requirement in wireless multi-hop networks because nodes failure may disconnect other active nodes. Minimum s-t cuts can help to measure the reliability of a network regarding the nodes or links failure. A minimum s-t cut is the smallest subset of links that their failure disconnects all communication paths between nodes s and t. Minimum s-t cuts can also reveal the bottlenecks, bridges, and clusters in the network. This paper proposes an asynchronous distributed algorithm for finding minimum s-t cuts in wireless multi-hop networks. The proposed algorithm iteratively finds link-disjoint paths from s to t and changes the direction of the selected edges to ignore them in the next iteration. After finding all paths, the undiscovered nodes in the last search determine the minimum s-t cut. The comprehensive simulation results on different networks with up to 500 nodes show that the proposed algorithm finds minimum s-t cuts in reasonable time with up to 64% and 39% lower energy consumption than the existing central and distributed algorithms, respectively.

Modified Dual-Path Allocation Algorithm in Elastic Optical Networks

Dual-path allocation problem is considered to be a case of multipath routing in Elastic Optical Networks. In this article, the optimization problem is formulated and a dual-path allocation algorithm that solves this problem proposed. In the considered problem all traffic for each request is broken into two equal parts, which are directed along two link-disjoint paths. After any link failure, half of the traffic for each affected request is realized. The proposed algorithm is based on the two weight matrices: the elements of the first one depend on the actual length of the links and their utilization, while the elements of the second one assume unit values if the links exist in the network. The proposed algorithm rejects smaller requests and provides a much lower bandwidth blocking probability than other analyzed algorithms.

Modulation-Adaptive Link-Disjoint Path Selection Model for 1 + 1 Protected Elastic Optical Networks

In elastic optical networks (EONs), an appropriate modulation technique is adapted according to the distance of an optical path. A robust modulation technique with a large number of spectrum slots is considered for longer distance optical paths, and a less robust modulation technique with a small number of spectrum slots is used for shorter distance optical paths. When an optical path is configured, the number of required spectrum slots is determined based on the nonlinear relationship between the optical path length and the number of utilized spectrum slots. Minimizing the total path lengths does not always minimize the total number of required spectrum slots for configuring an optical path, which decreases the spectrum utilization. This paper introduces a modulation-adaptive link-disjoint path selection model by considering a step function based on realistic modulation formats in order to minimize the total number of utilized spectrum slots in 1 + 1 protected EONs. We formulate the modulation-adaptive link-disjoint path selection problem as an integer linear programming (ILP). We prove that the modulation-adaptive link-disjoint path selection problem is NP-complete. By using an optimization solver, we solve the ILP problem for different backbone networks, namely, Japan Photonic Network (JPN48), German 17 Network, and COST 239 Network, within a practical time. Numerical results obtained from performance evaluation indicate that the introduced model reduces the number of utilized spectrum slots compared to the conventional schemes.

Multipath Cooperative Routing with Efficient Acknowledgement for LEO Satellite Networks

Multipath routing can significantly improve the network throughput and end-to-end (e2e) delay. Network coding based multipath routing removes the complicated coordination among multiple paths so that it further enhances data transmission efficiency. Traditional network coding based multipath routing protocols, however, are inefficient for Low Earth Orbit (LEO) satellite networks with the long link delay and regular network topology . Considering these characteristics, in this paper, we first formulate the multipath cooperative routing problem, then propose a Network Coding based Multipath Cooperative Routing (NCMCR) protocol for LEO satellite networks to improve the throughput. We propose source-based and destination-based multipath cooperative routing algorithms, which deliver different parts of a data flow along multiple link-disjoint paths dynamically and cooperatively. Furthermore, we design an efficient No-Stop-Wait ACK mechanism for our NCMCR protocol to accelerate the data transmission, where a source node continuously sends subsequent batches before it receives ACK messages for the batches sent previously. Under the proposed acknowledgement mechanism, we theoretically analyze the number of coded packets that should be sent and the transmission times of each batch for successfully decoding a batch. NS2-based simulation results demonstrate that our NCMCR outperforms the most related protocols.

Minimum-Weight Link-Disjoint Node-“Somewhat Disjoint” Paths

Network survivability has been recognized as an issue of major importance in terms of security, stability and prosperity. A crucial research problem in this context is the identification of suitable pairs of disjoint paths. Here, “disjointness” can be considered in terms of either nodes or links. Accordingly, several studies have focused on finding pairs of either link or node disjoint paths with a minimum sum of link weights. In this paper, we investigate the gap between the optimal node-disjoint and link-disjoint solutions. Specifically, we formalize several optimization problems that aim at finding minimum-weight link-disjoint paths while restricting the number of its common nodes. We establish that some of these variants are computationally intractable, while for other variants we establish polynomial-time algorithmic solutions. Finally, through extensive simulations, we show that, by allowing link-disjoint paths share a few common nodes, a major improvement is obtained in terms of the quality (i.e., total weight) of the solution.

A Novel Dedicated Route Protection Scheme for Survivability of Link Failure in Elastic Optical Networks

The spectrally efficient transportation of the high bit rate(s) data is achievable by the Elastic optical networks (EONs). However, in the EONs, owing to the failure occurrence even in an individual simple element, different service(s) maybe interrupted. Hence, it is imperative that the schemes for survivability be developed so that the issues due to the possible failure(s) can be overcome. In the current work, in view of survivability of the link failure(s) in the EONs, we propose the Spectrum Continuity and Contiguity Established DRP (SCC-E-DRP) algorithm which is a novel dedicated route protection (DRP) scheme that attempts to avoid the problem of trap topology during its exploration for a pair of link disjoint path. Further, to evaluate the link disjoint paths, we resort to the use of the SCC Established Shortest Route (SCC-E-SR) algorithm which is a modified Dijkstra’s algorithm based scheme that selects the path(s) pair(s) based on the end-toend SCC. We conduct extensive simulations considering realistic network topologies, and compare the performance of the SCCE-DRP scheme with the existing techniques. The obtained results show that, compared to the existing schemes, the SCC-E-DRP scheme achieves better results in terms of blocking probability.

Spectrum efficient distance-adaptive paths for fixed and fixed-alternate routing in elastic optical networks

Abstract Efficient utilization of spectrum is a key concern in the soon to be deployed elastic optical networks (EONs). To perform routing in EONs, various fixed routing (FR), and fixed-alternate routing (FAR) schemes are ubiquitously used. FR, and FAR schemes calculate a fixed route, and a prioritized list of a number of alternate routes, respectively, between different pairs of origin o and target t nodes in the network. The route calculation performed using FR and FAR schemes is predominantly based on either the physical distance, known as k -shortest paths (KSP), or on the hop count (HC). For survivable optical networks, FAR usually calculates link-disjoint (LD) paths. These conventional routing schemes have been efficiently used for decades in communication networks. However, in this paper, it has been demonstrated that these commonly used routing schemes cannot utilize the network spectral resources optimally in the newly introduced EONs. Thus, we propose a new routing scheme for EON, namely, k -distance adaptive paths (KDAP) that efficiently utilizes the benefit of distance-adaptive modulation, and bit rate-adaptive superchannel capability inherited by EON to improve spectrum utilization. In the proposed KDAP, routes are found and prioritized on the basis of bit rate, distance, spectrum granularity, and the number of links used for a particular route. To evaluate the performance of KSP, HC, LD, and the proposed KDAP, simulations have been performed for three different sized networks, namely, 7-node test network (TEST7), NSFNET, and 24-node US backbone network (UBN24). We comprehensively assess the performance of various conventional, and the proposed routing schemes by solving both the RSA and the dual RSA problems under homogeneous and heterogeneous traffic requirements. Simulation results demonstrate that there is a variation amongst the performance of KSP, HC, and LD, depending on the o - t pair, and the network topology and its connectivity. However, the proposed KDAP always performs better for all the considered networks and traffic scenarios, as compared to the conventional routing schemes, namely, KSP, HC, and LD. The proposed KDAP achieves up to 60 % , and 10.46 % improvement in terms of spectrum utilization, and resource utilization ratio, respectively, over the conventional routing schemes.

An offline scheme for reducing cost of protection in all-optical WDM mesh networks with fast recovery

ABSTRACTIn Optical WDM networks, a single fiber carries enormous amount of data and consequently designing schemes to prevent the user traffic from disruption and techniques to recover from failures still remains an important area of research. In this paper we address the problem of protecting all-optical WDM mesh networks from single link failure. We propose an offline protection scheme that is not only cost-efficient in terms of network resource consumption but can also provide quick recovery from a link failure. In our scheme, backup paths are combined to reduce cost of protection and to facilitate fast recovery from a failure. We address a critical issue related to selection of backup paths to be combined, which was not addressed earlier. Instead of choosing backup paths for connection requests arbitrary as done in an existing scheme, our scheme is designed to select backup paths in a way that they are suitable for combination and can maximize resource saving as well. We first provide an Integer Linear Program for the problem, and then propose a heuristic eStreams that can provide near optimal solution in polynomial time. Performance comparisons with some well-known schemes show that our protection scheme is definitely an improvement in terms resource conservation while ensuring fast recovery from a link failure.The figure shows how a primary (working) path is protected with the help of a link-disjoint backup path in WDM optical networks. A primary path is used to carry traffic under normal fault free condition. In the event of a link fault (fiber-cut) the traffic is switched over to the backup path.

On the combinatorial design of data centre network topologies

The theory of combinatorial designs has recently been used in order to build switch-centric data centre networks incorporating a large number of servers, in comparison with the popular Fat-Tree data centre network. We clarify and extend these results and prove that in these data centre networks: there are pairwise link-disjoint paths joining all the servers adjacent to some switch with all the servers adjacent to any other switch; and there are pairwise link-disjoint paths from all the servers adjacent to some switch to any identically-sized collection of target servers where these target servers need not be adjacent to the same switch. In both cases, we always control the path lengths. Our constructions and analysis are undertaken on bipartite graphs with the applications to data centre networks being easily derived. Our results show the potential of the application of results and methodologies from combinatorics to data centre network design.

Reliable Virtual Machine Placement and Routing in Clouds

In current cloud computing systems, when leveraging virtualization technology, the customer's requested data computing or storing service is accommodated by a set of communicated virtual machines (VM) in a scalable and elastic manner. These VMs are placed in one or more server nodes according to the node capacities or failure probabilities. The VM placement availability refers to the probability that at least one set of all customer's requested VMs operates during the requested lifetime. In this paper, we first study the problem of placing at most H groups of k requested VMs on a minimum number of nodes, such that the VM placement availability is no less than $\delta$, and that the specified communication delay and connection availability for each VM pair under the same placement group are not violated. We consider this problem with and without Shared-Risk Node Group (SRNG) failures, and prove this problem is NP-hard in both cases. We subsequently propose an exact Integer Nonlinear Program (INLP) and an efficient heuristic to solve this problem. We conduct simulations to compare the proposed algorithms with two existing heuristics in terms of performance. Finally, we study the related reliable routing problem of establishing a connection over at most w link-disjoint paths from a source to a destination, such that the connection availability requirement is satisfied and each path delay is no more than a given value. We devise an exact algorithm and two heuristics to solve this NP-hard problem, and evaluate them via simulations.

Energy aware routing with link disjoint backup paths

Energy aware routing has attracted a wide spread attention in the last decade. However, relatively concentrated traffic after applying energy aware strategies makes the network be vulnerable to link failure and sudden traffic bursts. It is a challenge to take enhancing network reliability into account while keeping low energy consumption. Routing each source-to-terminal request via two disjoint paths can be a trade-off. In this paper, we propose a problem called Energy Aware Routing with Link Disjoint Backup Paths (EAR-LDBP) to minimize router power consumption when backup sharing is not allowed during off-peak hours. Each request is routed via an active path. A link disjoint backup path is computed for each request and can be used to route traffic in case of single link failure on the active path. A 0–1 integer linear programming model that can guarantee the network resilience to single link failure is formulated to minimize the power of used links and nodes while putting idle ones to sleep under constraints of link utilization and a link disjoint backup path for each request. We analyze the complexity of EAR-LDBP and show its Np-hardness. We prove that there is no polynomial-time constant-factor approximation algorithm even for two requests. Four different versions of EAR-LDBP (link/node-disjoint, link cost only/link and node cost) are shown to be equivalent and polynomial-time reducible to each other. Then two algorithms are proposed to solve this problem: 2 Stage Greedy Algorithm (2SG) and Greedy Two Link Disjoint Paths Algorithm (G2DP) with an iterative deletion strategy to improve the solution. For comparison purpose, we also use the state of the art reliable energy aware routing algorithm 2DP-NF in unsplittable way. Simulation results on synthetic networks and real network of Internet2 show the effectiveness of our algorithms. Particularly, our algorithms can save more energy (up to 39%) while using less computation time as compared to 2DP-NF (less than 1% at best).

Parallel and survivable multipath circuit provisioning in ESnet’s OSCARS

Data generation is approaching petascale and exascale rates by cutting-edge science and research applications varying from material informatics to physics. With data generation and management comes the necessity to transmit such vast collections of information across the world's networks for processing, analysis, storage, or peer-sharing. This practice is becoming the norm to the large-scale scientific community, but complications can arise during networking. There are countless situations such as component failure due to a harmless construction accident or a devastating natural disaster that may lead to catastrophic interruption of service. Furthermore, given the size of datasets, there is a strong need to support intelligent and fast parallelism throughout the network to allow end users to efficiently consume available bandwidth. We therefore propose a multipath extension for ESnet's On-demand Secure Circuits and Advance Reservation System (OSCARS), the network research community's most popular long-lived circuit-provisioning software package. Presently, OSCARS supports purely point-to-point circuits; however, our proposed client software provides an overlay onto the default OSCARS path computation engine that enables end users to route their data along multiple link-disjoint paths to provide session survivability and increase the degree of parallelism. We have also adapted the proposed multipath extension to an existing anycast OSCARS deployment, which allows for the selection of one preferred destination node from among a set of potential candidates. Through thorough simulation analysis and exposure to realistic failure event distributions, we quantitatively evaluate the multipath client performance and showcase the relative benefits when compared to the standard single-path OSCARS deployment.

Joint relay assignment and rate–power allocation for multiple paths in cooperative networks

Multi-path transmission is an efficient way to balance the power consumption from a source to a destination. The previous works have studied rate---power allocation to prolong the network lifetime of multiple paths. As at least one relay node is required to participate into cooperative transmission, its assignment will greatly impact the power consumption of cooperative communication. Thus, this paper addresses the joint resource allocation problem which aims to prolong the lifetime of multi-path cooperative transmission. Given a path set from a source to a destination, we first define the lifetime-optimal relay assignment and rate---power allocation problem (LRRP) for multiple paths with cooperative communications. This paper then presents two heuristic algorithms, called BS-RRP and PS-RRP, to implement efficient resource allocation for multiple paths. The BS-RRP algorithm uses the binary search method to solve the LRRP problem on node-disjoint paths, and reaches the approximate performance 1 ? ?, where ? is an arbitrarily small positive constant. PS-RRP adopts the pattern search method for joint resource allocation on link-disjoint paths, and terminates after finite iterations. The simulation results show that the BS-RRP and PS-RRP algorithms can improve the network lifetimes about 26 and 30 % compared with the resource allocation methods under the non-cooperative communication scheme.

Toggling dual label: an exact algorithm for finding the optimal pair of link-disjoint paths in $$\alpha +1$$ α + 1 path protection

Most network real-time applications require reliable transmission against incidents such as link failure. Path protection utilizes a link-disjoint secondary path to protect the primary path. Nevertheless, existing path protection schemes have drawbacks in either resource utilization or recovery response from link failure for real-time services. Recently, the $$\alpha +1$$?+1 protection was proposed to provide partial bandwidth protection for mission critical data only. The $$\alpha +1$$?+1 protection enables fast recovery from link failure with efficient resource utilization. However, finding the optimal pair of primary-secondary paths for $$\alpha +1$$?+1 protection remains a challenge. Existing paths-finding algorithms for the $$\alpha +1$$?+1 protection utilize the $$K$$K-shortest path approach, considerably increasing the algorithm's complexity. This paper presents a novel exact $$\alpha +1$$?+1 path-finding algorithm, called the Toggling Dual Label algorithm, to efficiently identify the optimum solution in polynomial time without utilizing the $$K$$K-shortest path algorithm. The proposed algorithm is shown to produce the optimum solution while maintaining a low complexity.

Energy-Aware Multipath Routing Scheme Based on Particle Swarm Optimization in Mobile Ad Hoc Networks.

Mobile ad hoc network (MANET) is a collection of autonomous mobile nodes forming an ad hoc network without fixed infrastructure. Dynamic topology property of MANET may degrade the performance of the network. However, multipath selection is a great challenging task to improve the network lifetime. We proposed an energy-aware multipath routing scheme based on particle swarm optimization (EMPSO) that uses continuous time recurrent neural network (CTRNN) to solve optimization problems. CTRNN finds the optimal loop-free paths to solve link disjoint paths in a MANET. The CTRNN is used as an optimum path selection technique that produces a set of optimal paths between source and destination. In CTRNN, particle swarm optimization (PSO) method is primly used for training the RNN. The proposed scheme uses the reliability measures such as transmission cost, energy factor, and the optimal traffic ratio between source and destination to increase routing performance. In this scheme, optimal loop-free paths can be found using PSO to seek better link quality nodes in route discovery phase. PSO optimizes a problem by iteratively trying to get a better solution with regard to a measure of quality. The proposed scheme discovers multiple loop-free paths by using PSO technique.