Node-disjoint Paths Research Articles

Optimal construction of node-disjoint shortest paths in folded hypercubes

Node-disjoint paths have played an important role in the study of routing, reliability, and fault tolerance of an interconnection network. In this paper, we give a necessary and sufficient condition, which can be verified in O(mn1.5) time, for the existence of m node-disjoint shortest paths from one source node to other m (not necessarily distinct) target nodes, respectively, in an n-dimensional folded hypercube, where m≤n+1. Moreover, when the condition holds, the m node-disjoint shortest paths can be constructed in optimal O(mn) time. In the situation that all of the source node and target nodes are mutually distinct, brute-force computations show that the probability of existence of the m node-disjoint shortest paths in an n-dimensional folded hypercube is not less than 100%, 86%, 86%, 92%, and 94% for (n,m)=(3,4),(4,4),(5,6),(6,6), and (7, 8), respectively.

Bandwidth scheduling for big data transfer using multiple fixed node-disjoint paths

Many large-scale applications require the transfer of big data over high-performance networks for remote operations. Such requirements call for a fast bandwidth scheduling solution to discover feasible and efficient reservation options in network environments with time-varying bandwidths. We formulate a generic problem of Bandwidth Scheduling with Two Node-Disjoint Paths (BS-2NDP) to support big data transfer. In BS-2NDP, we further consider two different types of paths: (i) two fixed paths with fixed bandwidth (2FPFB), and (ii) two fixed paths with variable bandwidth (2FPVB). We prove that both 2FPFB and 2FPVB are NP-complete, and design a heuristic approach for each of them. We implement and evaluate these scheduling algorithms in both simulated and real-life networks. Extensive results show that the proposed heuristics achieve a close-to-optimal performance in small-scale networks, and significantly outperform other heuristic approaches in large-scale networks.

Topology Control for Guaranteed Connectivity Provisioning in Heterogeneous Sensor Networks

Topology control is important for heterogeneous sensor networks in order to minimize the total network power consumption under the constraint that all sensor nodes’ connectivity requirements are satisfied. To address this issue, an optimization problem is first formulated, which is formally proved to be NP-hard. For practical applications, an effective solution, named topology adaptation algorithm (TAA), is proposed. TAA adopts both graph theory and maximum flow theory to find prespecified node disjoint paths with low time complexity and high network power efficiency. In order to further save the network power consumption, a judgment theory is proposed to remove any unnecessary long edges at the beginning without affecting network connectivity. Both theoretical and numeric results show that the proposed topology control algorithm can outperform counterparts in terms of the total network power consumption, the percentage of supernodes achieving $k$ -connectivity, the average degree of nodes, and the average length of paths.

Joint cost and secured node disjoint energy efficient multipath routing in mobile ad hoc network

The severe resource constraints and deployment environments of mobile ad hoc networks (MANETs) pose challenges for the security and energy consumption during data transmission for these networks. Multipath routing and energy consumption are the important factors to be considered in mobile ad hoc network as it provides a powerful tool for studying security aspects during data transmission. Advances in MANET technology have provided the availability of energy efficient reliable and multi path routing for intrusion tolerance with capability of identifying reliable routes, determining the best redundancy level to increase the operational lifetime of the network. Identifying a secured and energy efficient multipath routing for MANET represents the basic challenge during data transmission. In order to overcome such limitation, a hybrid method called as joint cost and secured node disjoint energy-efficient multipath routing (NDE-MR) is designed for MANET to reduce the energy consumption and execution time during the multipath routing and to improve security during data transfer. Node initialization initializes the mobile nodes with energy efficient model by obtaining the neighbor node data. Next, cost-based multipath route discovery model identifies the path with the least transmission cost through which data forwarding is made. Finally, security is achieved through node disjoint path model by splitting the data packets into different segments. Simulation results show that the NDE-MR model is able to reduce energy consumption and execution time during multipath routing and to increases the security of the network.

Algorithms for determining a node-disjoint path pair visiting specified nodes

The problem of calculating the shortest path that visits a given set of nodes is at least as difficult as the traveling salesman problem, and it has not received much attention. Nevertheless an efficient integer linear programming (ILP) formulation has been recently proposed for this problem. That ILP formulation is firstly adapted to include the constraint that the obtained path can be protected by a node-disjoint path, and secondly to obtain a pair of node disjoint paths, of minimal total additive cost, each having to visit a given set of specified nodes. Computational experiments show that these approaches, namely in large networks, may fail to obtain solutions in a reasonable amount of time. Therefore heuristics are proposed for solving those problems, that may arise due to network management constraints. Extensive computational results show that they are capable of finding a solution in most cases, and that the calculated solutions present an acceptable relative error regarding the cost of the obtained path or pair of paths. Further the CPU time required by the heuristics is significantly smaller than the required by the used ILP solver.

Energy-aware data center networks

With developing on cloud computing, data center networks have received great attention recently. In order to support high availability and bandwidth, data center networks are usually designed based on peak traffic. Unfortunately, peak traffic does not happen all the time. This causes unnecessary energy wastage and leads to low network utilization. We aim to minimize the power usage of data center networks by consolidating traffic flows and turning off unnecessary network devices. To support high availability, a requirement of two node-disjoint paths between the source and destination of each traffic flow is considered. We formulate the problem in mathematical format by integer linear programming (ILP). Due to its high computational complexity, we further propose a heuristic approach for practical use. The experimental results show that the heuristic approach reduces the power consumption by 15 to 35% in average while improving the availability by about 15% with significant improvement on computation time.

Two node-disjoint hop-constrained survivable network design and polyhedra

Given a weighted undirected graph G with a set of pairs of terminals (si, ti), i = 1 , … , d , and an integer L ≥ 2 , the two node-disjoint hop-constrained survivable network design problem is to find a minimum weight subgraph of G such that between every si and ti there exist at least two node-disjoint paths of length at most L. This problem has applications in the design of survivable telecommunication networks with QoS-constraints. We discuss this problem from a polyhedral point of view. We present several classes of valid inequalities along with necessary and/or sufficient conditions for these inequalities to be facet defining. We also discuss separation routines for these classes of inequalities, and propose a Branch-and-Cut algorithm for the problem when L = 3, as well as some computational results. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 67(4), 316–337 2016

Scheduled-links multicast routing protocol in MANETs

Dynamically changing of network topology due to node movement is considered a main challenge in providing reliable and low-cost paths in one to many ends of communication in mobile ad hoc networks. To address this challenge, this paper proposes a scheduled-links multicast routing protocol (SLMRP) based on mobility prediction. SLMRP constructs multiple scheduled paths between multicast sources and receivers. SLMRP scheduled paths are subject to reliability and quality of service requirements in load-balance strategy. Multiple loop-free and node-disjoint paths are constructed for each source–receiver pair during route discovery process. To control the activation and deactivation of these paths, we introduce multicast routing activation timer (MRAT) and path timeout timer (PTT). MRAT and PTT are computed according to the route expiration time for the set of the discovering paths. Performance comparison results demonstrate that the proposed protocol outperforms PUMA, MAODV, and PMRP.

On the construction of all shortest node-disjoint paths in star networks

Node-disjoint paths have played an important role in the study of routing, reliability, and fault tolerance of an interconnection network. In this paper, we give a sufficient condition, which can be verified in O(mn1.5) time, for the existence of m node-disjoint shortest paths from one source node to other m (not necessarily distinct) target nodes, respectively, in an n-dimensional star network, where m≤n−1 and n≥3. In addition, when the condition holds, the m node-disjoint shortest paths can be constructed in optimal O(mn) time. By the aid of the sufficient condition, the probability of existence of all shortest node-disjoint paths was also evaluated for some special cases.

Full Protection Made Easy: The DisPath IP Fast Reroute Scheme

A major concern in IP networks is to ensure that any topology changes, whether planned or unplanned, do not disrupt network performance. IP Fast Reroute (IP FRR) is a general approach to address this issue by promptly forwarding an IP packet to a predetermined alternate next-hop as soon as the primary next-hop to the destination becomes unavailable. Among the numerous IP FRR schemes proposed to date, the simplest ones do not guarantee protection against every component failure, while more sophisticated ones tend to be difficult to implement due to various inherent complexities, such as nontrivial modifications of IP packets or high resource requirements. This paper presents a simple and efficient IP FRR scheme called DisPath, which leverages several fundamental properties of minimum-cost node-disjoint paths for determining the alternate next-hop toward a given destination. We show that DisPath ensures full coverage, meaning protection against all single link or node failures, with low computational overhead and without the practical complications encountered by other schemes that offer the same level of protection. Our simulations on several realistic instances reveal that DisPath usually creates shorter (and, at worst, not much longer) alternative paths than existing solutions adopted by the industry. Combined with the aforementioned protection guarantee and simplicity of implementation, these results provide strong evidence that DisPath is a most compelling choice of IP FRR scheme.

Fault resilience in sensor networks: Distributed node-disjoint multi-path multi-sink forwarding

Sensor network deployed for the critical infrastructure monitoring requires high degree of reliability in sensory data gathering, in spite of arbitrary node or sink failures. This paper proposes a robust data gathering scheme specially designed to provide guaranteed delivery of the sensory data for applications on the critical infrastructure monitoring. Redundancy in a sensor network, in terms of both the number of deployed sensors and the amount of duplicate data delivery, is explored to design an effective protocol that ensures the reliable data delivery while assuring the timeliness, connectivity and the sensing coverage. A set of active sensors is selected from all the sensors deployed, based on the network connectivity and the sensing coverage criteria that participates in the data forwarding process. Rest of the sensors go to the sleep state, and act as a replacement on the failure of an active sensor. The proposed protocol aims to find out multiple node-disjoint paths to multiple sinks, so that the loss of connectivity in one path due to node failure does not disrupt application services. The effectiveness of the proposed scheme has been analyzed using simulation results, and compared with other protocols proposed in the literature for reliable data delivery.

Fault-tolerant routing over shortest node-disjoint paths in hypercubes

This paper presented a routing algorithm that finds n disjoint shortest paths from the source node s to target node d in the n-dimensional hypercube. Fault-tolerant routing over all shortest node-disjoint paths has been investigated to overcome the failure encountered during routing in hypercube networks. In this paper, we proposed an efficient approach to provide fault-tolerant routing which has been investigated on hypercube networks. The proposed approach is based on all shortest node-disjoint paths concept in order to find a fault-free shortest path among several paths provided. The proposed algorithm is a simple uniform distributed algorithm that can tolerate a large number of process failures, while delivering all n messages over optimal-length disjoint paths. However, no distributed algorithm uses acknowledgement messages (acks) for fault tolerance. So, for dealing the faults, acknowledgement messages (acks) are included in the proposed algorithm for routing messages over node-disjoint paths in a hypercube network.

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.

Efficient data transfer in mobile ad-hoc network using OPSM for disaster response applications

The nodes in mobile ad-hoc network depend on battery for its power. Therefore, effective utilization of energy is necessary for efficient transfer of data between the persons involved in rescue without connection termination in disaster situation. An Optimal Path Selection Model (OPSM) is proposed to achieve this. First, routes are identified with the links having high power ratio and link duration. The path selection aims at reducing the number of node failures which in turn obtains energy saving. Then, the source will select a node-disjoint path based on energy and hop for data transfer and store the remaining paths in cache. Priority based path maintenance is also proposed for the selection of routes from cache based on remaining energy if the primary selection fails. Path selection and maintenance extend the network lifetime by reducing the energy usage in transmission. Simulation results revealed that OPSM achieves 64% and 50% reduction in energy consumption compared to Dynamic Source Routing (DSR) and Multipath DSR (MDSR). The number of path breakages is also 11 times and 5.5 times lesser than DSR and MDSR. Thus, it can be said that OPSM is a better choice for optimal path selection for performance enhancement by saving energy and improving lifetime. All Rights Reserved © 2015 Universidad Nacional Autonoma de Mexico, Centro de Ciencias Aplicadas y Desarrollo Tecnologico. This is an open access item distributed under the Creative Commons CC License BY-NC-ND 4.0.

QoS Routing Protocol with Multiple Node-Disjoint Paths in Ad Hoc Networks

Quality-of-service (QoS) routing in dynamic, wireless multi-hop ad hoc networks is a critical research issue, and various QoS protocols are proposed. However, those QoS routing protocols rarely provide multiple routes. Once links break, it takes time and brings large control overhead to establish new routes. This paper proposes a new QoS routing protocol, containing efficient bandwidth estimations, admission control and node-disjoint multi-path establishment. While detecting link breaks, we use back-up routes to avoid making wasteful route discovery. If a single route with sufficient bandwidth cannot be discovered, we propose to combine multiple routes to support QoS transmission. Simulation results show that the proposed QoS routing protocol increases throughput while provides satisfactory QoS.

A New Zone Disjoint Multi Path Routing Algorithm to Increase Fault-Tolerant in Mobile Ad Hoc Networks

In Mobile Ad-hoc Networks, there is no fixed infrastructure, router and station and so all network operations such as routing are being done with nodes. Some routing algorithms of Mobile Ad-hoc Networks perform routing in a multi-path manner and simultaneously discover and record a number of paths in a path discovery process. In these algorithms, it is possible to s end information to destination concurrently using several paths, in order t o balance the load in the network, increase end to end bandwidth, and decrease delay. In this case, selecting node disjoint paths is one of t he best options because of increasing error tolerability. G iven channel access mechanisms, sending information through completely disjoint paths is not fully independent. To solve the problem, we can use zone disjoint paths rather than node disjoint paths. Two paths are fully zone disjoint ones if none of the nodes in a path is adjacent to the nodes in the other. Methods have been proposed to discover zone disjoint paths; one of them is using directional antennas but these are not available in most of current facilities. The other method is Zone Disjoint Ad-hoc On-demand Multipath Distance (ZD AOMDV) which has high overload while routing and additionally we see the very high delay during path discovery phase. A new method will be proposed in this paper which has been applied in the proposed algorithm Improved Zone Multipath Ad-hoc On- demand Distance Vector (IZM AODV). In the algorithm, it is possible to discover zone disjoint paths using typical, omnidirectional antennas with minimum overload and delay in path discovery phase. In addition, these paths are used to send information concurrently. The proposed algorithm has been simulated in different scenarios using NS2 software and it has been examined and compared with multipath algorithms (AOMDV and ZD AOMDV) and basic algorithm (AODV). Routing overloads, sending packets successfully, and end to end delays have been improved compared to existing methods.

A Routing Algorithm Solving the Container Problem in a Hypercube with Bit Constraint

As reflected by the TOP500 list, hypercubes are popular interconnection networks for massively parallel systems, the main reason being the simplicity and ease of implementation of this network topology. In order to retain performance high and avoid bottleneck situation, routing algorithms are critical for these high-performance systems. Furthermore, disjoint path routing is a very desirable property of such communication algorithms. Effectively, selecting mutually node-disjoint paths guarantees that notorious parallel processing issues such as deadlocks, livelocks and starvations shall never occur. In this paper, we describe a routing algorithm for hypercubes that, given a bit constraint, selects internally node-disjoint paths between any pair of nodes satisfying the constraint, and such that the selected paths all satisfy the constraint. The introduction of such bit constraint enables the selection of multiple sets of disjoint paths between several node pairs each satisfying a distinct bit constraint, which is impossible with conventional routing algorithms. Selecting simultaneously disjoint paths between different node pairs induces increased communication performance and system dependability. The correctness and complexities of the described algorithm are formally proved, and analysis of the algorithm performance in practice is conducted by empirical evaluation.

An Optimal Inherently Stabilizing Algorithm for Routing over All Node-Disjoint Paths in Exchanged Hypercubes

An Optimal Inherently Stabilizing Algorithm for Routing over All Node-Disjoint Paths in Exchanged Hypercubes

Survivable Virtual Infrastructure Mapping With Dedicated Protection in Transport Software-Defined Networks [Invited

Efficiently mapping multiple virtual infrastructures (VIs) onto the same physical substrate with survivability is one of the fundamental challenges related to network virtualization in transport software-defined networks (T-SDNs). In this paper, we study the survivable VI mapping problem in T-SDNs with the objective of minimizing the VI request blocking probability. In particular, we address the subproblems of modulation selection and spectrum allocation in the process of provisioning optical channels to support virtual links, taking into consideration the optical layer constraints such as the transmission reach constraint and the spectral continuity constraint. We propose an auxiliary-graph-based algorithm, namely, parallel VI mapping (PAR), to offer dedicated protection against any single physical node or link failure. More specifically, the PAR algorithm can jointly optimize the assignments of mapping the primary and backup VIs by adopting the modified Suurballe algorithm to find the shortest pair of node-disjoint paths for each virtual link. Through extensive simulations, we demonstrate that the PAR algorithm can significantly reduce the VI request blocking probability and improve the traffic-carrying capacity of the networks, compared to the baseline sequential VI mapping approaches.

One-to-one disjoint path covers on alternating group graphs

The alternating group graph, denoted by AGn, is one of the popular interconnection networks, which has many attractive properties. In this paper, we prove that for any two distinct nodes μ and ν, there exist m node-disjoint paths for any integer n≥3 with 1≤m≤2n−4 whose union covers all the nodes of AGn. For any node of AGn has exactly 2n−4 neighbors, 2n−4 is the maximum number of node-disjoint paths can be constructed in AGn.