Finding all hops shortest paths

In this letter, we introduce and investigate a new problem referred to as the All Hops Shortest Paths (AHSP) problem. The AHSP problem involves selecting, for all hop counts, the shortest paths from a given source to any other node in a network. We derive a tight lower bound on the worst-case computational complexities of the optimal comparison-based solutions to AHSP.     

Alternative shortest paths in n-cubes

Explicit expressions are given for the number of shortest paths between any two vertices in an n-cube, each path being otherwise vertex disjoint from any specified shortest path between the same pair of vertices, and for the probability of randomly selecting one of these alternative paths     

DT-MRI fiber tracking: a shortest paths approach

We derive a new fiber tracking algorithm for DT-MRI that parts with the locally “greedy” paradigm intrinsic to conventional tracking algorithms. We demonstrate the ability to precisely reconstruct a diverse range of fiber trajectories in authentic and computer-generated DT-MRI data, for which well-known conventional tracking algorithms are shown to fail. Our approach is to pose fiber tracking as a problem in computing shortest paths in a weighted digraph. Voxels serve as vertices, and edges are included between neighboring voxels. We assign probabilities (weights) to edges using a Bayesian framework. Higher probabilities are assigned to edges that are aligned with fiber trajectories in their close proximity. We compute optimal paths of maximum probability using computationally scalable shortest path algorithms. The salient features of our approach are: global optimality—unlike conventional tracking algorithms, local errors do not accumulate and one “wrong-turn” does not spell disaster; a target point is specified a priori; precise reconstruction is demonstrated for extremely low signal-to-noise ratio; impartiality to which of two endpoints is used as a seed; and, faster computation times than conventional all-paths tracking. We can use our new tracking algorithm in either a single-path tracking mode (deterministic tracking) or an all-paths tracking mode (probabilistic tracking).      

An efficient algorithm for virtual-wavelength-path routing minimizing average number of hops

We present a novel heuristic algorithm for routing and wavelength assignment in virtual-wavelength-path (VWP) routed wavelength-division multiplexed optical networks. We are the first to take up the approach of both minimizing the network cost, as well as maximizing the resource utilization. Our algorithm not only minimizes the number of wavelengths required for supporting the given traffic demand on any given topology, but also aims to minimize the mean hop length of all the lightpaths which in turn maximizes the resource utilization. The algorithm initially assigns the minimum hop path to each route and then performs efficient rerouting to reduce the number of wavelengths required while also trying to minimize the average hop length. To further reduce the network cost, we also propose a wavelength assignment procedure for VWP routed networks which minimizes the number of wavelength converters required. Our algorithm has been tested on various topologies for different types of traffic demands and has been found to give solutions much better than previous standards for this problem.     

基于最短路径数的网络抗毁评价方法

由于全连通网络具有最强的抗毁性,且节点间最短路径数对于网络抗毁性有重要意义,通过对计算节点之间的最短路径数,并将待评价网络与全连通网络进行结构差异比较,提出了一种基于最短路径数的网络抗毁评价方法.在此基础上建立了网络节点重要性的评价模型,一个节点与网络中其他节点之间的平均等效最短路径数越多,则该节点越重要.由于评价模型的关键是最短路径数的计算,因此,还提出了一种基于邻接阵的最短路径数计算方法.     

F-TPR: fine two-phase IP routing scheme over shortest paths for hose model

This letter proposes an IP-based finely-distributed routing scheme based on two-phase routing (TPR) over shortest paths for the hose model. It is called the fine-TPR (F-TPR) scheme. Compared to the original TPR, F-TPR distributes traffic from a source node to intermediate nodes more finely, where the distribution ratio is determined for each source-destination pair. To determine an optimum set of the distribution ratios, we successfully formulate our problem as a quadratic constraint programming (QCP) formulation that can be solved by using a mathematical programming solver. Numerical results show that F-TPR greatly outperforms TPR and its performance approaches that provided by the sophisticated traffic engineering (TE) scheme of multi-protocol label switching (MPLS-TE).     

An efficient multiple shortest augmenting paths algorithm for constructing high performance VLSI subarray

Reconfiguring a high-performance subarray of a VLSI array with faults is to construct a maximum target array with the minimum number of long interconnects, which can reduce communication costs, capacitance and dynamic energy dissipation. An existing work proved that the high performance VLSI subarray can be constructed in polynomial time using network flow algorithm. However, because of the disadvantage of the previous network model and the low-performing of standard network flow algorithms for reconfiguration, the efficiency of these algorithms is poor for constructing the high performance VLSI subarray. In this paper, we present an efficient multiple shortest augmenting paths algorithm for rapidly constructing high performance VLSI array. Firstly, we proposed an efficient data structure to construct the network model of the VLSI array with faults, which can dramatically reduce the size of the model compared with previous algorithm. Secondly, a multiple shortest augmenting path algorithm based on the new data structure is proposed, which can significant reduce the running time. Finally, we conduct solid experiments to highlight the efficiency of the proposed method in terms of the running time compared to the standard network flow algorithms. The experimental results show that on a 64 × 64 host array with 0.1% faults, the size of the network model can be reduced by about 50% and the average improvements in running time is up to 85.10% compared with four standard network flow algorithms.     

Constrained shortest link-disjoint paths selection: a network programming based approach

Given a graph G with each link in the graph associated with two positive weights, cost and delay, we consider the problem of selecting a set of k link-disjoint paths from a node s to another node t such that the total cost of these paths is minimum and that the total delay of these paths is not greater than a specified bound. This problem, to be called the constrained shortest link-disjoint path (CSDP(k)) problem, can be formulated as an integer linear programming (ILP) problem. Relaxing the integrality constraints results in an upper bounded linear programming problem. We first show that the integer relaxations of the CSDP(k) problem and a generalized version of this problem to be called the generalized CSDP (GCSDP (k)) problem (in which each path is required to satisfy a specified bound on its delay) both have the same optimal objective value. In view of this, we focus our work on the relaxed form of the CSDP(k) problem (RELAX-CSDP(k)). We study RELAX-CSDP(k) from the primal perspective using the revised simplex method of linear programming. We discuss different issues such as formulas to identify entering and leaving variables, anti-cycling strategy, computational time complexity etc., related to an efficient implementation of our approach. We show how to extract from an optimal solution to RELAX-CSDP(k) a set of k link-disjoint s-t paths which is an approximate solution to the original CSDP(k) problem. We also derive bounds on the quality of this solution with respect to the optimum. We present simulation results that demonstrate that our algorithm is faster than currently available approaches. Our simulation results also indicate that in most cases the individual delays of the paths produced starting from RELAX-CSDP(k) do not deviate in a significant way from the individual path delay requirements of the GCSDP(k) problem.     

Maximum number of independent paths and radio connectivity

Methods for determining the network reliability of a multihop packet radio network in the presence of hostile jammers are discussed. A new connectivity parameter called radio connectivity is defined as the maximum number of disjoint communication paths that are still usable between given nodes s and d after the jammer is on or, more generally, the minimum number of jammers needed to disconnect s and d. A lower bound on the radio connectivity is computed by studying the number of jamming independent paths. The time complexity of obtaining the radio connectivity is analyzed and shown to be NP-hard except for some special cases. Greedy heuristics for developing approximate answers for general networks are described. Euclidean networks, in which the nodes and links correspond to points and line segments in the Euclidean geometry and satisfy Euclid's four fundamental axioms, are also discussed. It is found that the maximum number of independent paths between a pair of source and destination nodes that can possibly exist is five. An extension in which there is a protected zone of known size around the sender and receiver is studied     

Butler network extension to any number of antenna ports

The addition of particular hybrid junctions to a conventional Butler network can increase the number of antenna ports from an integral power of 2 to any number. The resulting extended network produces greater flexibility in the relationship between the number of simultaneous beams and the radiation pattern.     

Parallel random number generators for sequences uniformly distributed over any range of integers

A VLSI design methodology is proposed for the efficient generation of multiple pseudorandom number sequences based on a simplification of Cauwenberghs' counterpropagation technique. We demonstrate that the counterpropagation of two sequences can be replaced by one propagating and one nonpropagating sequence, requiring as few as half the number of flip-flops, while still allowing new circuits to be added to the system without additional calculations-there is no need to keep track of random starting values, tap combinations, or time shifts. Moreover we extend our method from multiple bit sequences to multiple random number sequences that are uniformly distributed over any range of integers. In particular we address the more general problem of generating sequences over the range [0,K] where K+1 is any desired integer, including a power of two or a prime number. To this end we demonstrate that the simple concatenation of random bits to form random bytes is a special case of a more general concept whereby random integers distributed over prime number ranges are concatenated to form random integers distributed over any range. We find that the proposed design compares favorably with design strategies based on cellular automata, both in terms of statistical properties and implementation efficiencies.     

An efficient pursuit automata approach for estimating stable all‐pairs shortest paths in stochastic network environments

This paper presents a new solution to the dynamic all‐pairs shortest‐path routing problem using a fast‐converging pursuit automata learning approach. The particular instance of the problem that we have investigated concerns finding the all‐pairs shortest paths in a stochastic graph, where there are continuous probabilistically based updates in edge‐weights. We present the details of the algorithm with an illustrative example. The algorithm can be used to find the all‐pairs shortest paths for the ‘statistical’ average graph, and the solution converges irrespective of whether there are new changes in edge‐weights or not. On the other hand, the existing popular algorithms will fail to exhibit such a behavior and would recalculate the affected all‐pairs shortest paths after each edge‐weight update. There are two important contributions of the proposed algorithm. The first contribution is that not all the edges in a stochastic graph are probed and, even if they are, they are not all probed equally often. Indeed, the algorithm attempts to almost always probe only those edges that will be included in the final list involving all pairs of nodes in the graph, while probing the other edges minimally. This increases the performance of the proposed algorithm. The second contribution is designing a data structure, the elements of which represent the probability that a particular edge in the graph lies in the shortest path between a pair of nodes in the graph. All the algorithms were tested in environments where edge‐weights change stochastically, and where the graph topologies undergo multiple simultaneous edge‐weight updates. Its superiority in terms of the average number of processed nodes, scanned edges and the time per update operation, when compared with the existing algorithms, was experimentally established. Copyright © 2008 John Wiley & Sons, Ltd.     

On the distribution of the number of computations in any finite number of subtrees for the stack algorithm (Corresp.)

Multitype branching processes have been employed to determine the stack algorithm computational distribution for one subtree. These results are extended here to the distribution of the number of computations in any finite number of subtrees. Starting from the computational distribution forK-1subsequent subtrees, a recurrent equation for the distribution forKsubsequent subtrees is determined.     

Achieving full transmit diversity for PPM constellations with any number of antennas via double position and symbol permutations

We present a general technique for constructing minimal-delay rate-1 Space-Time (ST) block codes for Pulse Position Modulations (PPM) with an arbitrary number of transmit antennas. We show that the novel idea of time-domain constellation extension as well as introducing joint position and symbol permutations achieves a full transmit diversity order while maintaining unipolar transmissions. This renders the proposed scheme suitable for low-cost Time-Hopping Ultra- Wideband (TH-UWB) systems as well as Free-Space Optical (FSO) communications with direct detection.     

基于路径分解的关键路径求解方法

提出了一种求解关键路径的新方法,该方法基于路径分解的思想,对AOE网所有的路径进行分解,并利用多头单尾链表结构实现关键路径的求解。通过实例验证了算法的正确性。     

Distributed algorithms for computing shortest pairs of disjointpaths

Distributed algorithms for finding two disjoint paths of minimum total length from each node to a destination are presented. The algorithms have both node-disjoint and link-disjoint versions and provide each node with information sufficient to forward data on the disjoint paths. It is shown that this problem can be reduced to the problem of finding a minimal shortest path from each node to the destination in a modified network, and a distributed algorithm on the original network that simulates a shortest-paths algorithm running on the modified network is presented. The algorithm has a smaller space complexity than any previous distributed algorithm for the same problem, and a method for forwarding packets is presented that does not require any additional space complexity. A synchronous implementation of the algorithm is also presented and studied     

Adaptive reliability satisfaction in wireless sensor networks through controlling the number of active routing paths

The number of active paths in multipath routing scenarios (with concurrent data transmission over the established paths) affects the provided reliability degree as well as the imposed overhead of path management. Since the reliability of individual links varies over the time, adaptively setting the sufficient number of active paths turns out to be essential. In this paper, we first propose a Reliability Estimation for WSNs (RE-WSNs) algorithm, based on ordered binary decision diagram (OBDD) data structure, which gives the network reliability in terms of the reliability of all individual links. Second, we propose a novel algorithm called adaptive reliability satisfaction–multipath routing (ARS–MR) which adaptively sets the sufficient number of active paths, aiming at keeping the network reliability within a desired quantitative range and minimizing path management overhead. In activation/inactivation process it further takes into account energy efficiency considerations. The proposed ARS–MR algorithm can be used in conjunction with any arbitrary multipath algorithm in WSNs. Simulation results with NS-2 reveal that ARS–MR is quite successful in timely reacting to variations of links reliability. Indeed, it manages the number of active paths and keeps the reliability of the network satisfactory over the course of network lifetime.     

New dynamic algorithms for shortest path tree computation

The open shortest path first (OSPF) and IS-IS routing protocols widely used in today's Internet compute a shortest path tree (SPT) from each router to other routers in a routing area. Many existing commercial routers recompute an SPT from scratch following changes in the link states of the network. Such recomputation of an entire SPT is inefficient and may consume a considerable amount of CPU time. Moreover, as there may coexist multiple SPTs in a network with a set of given link states, recomputation from scratch causes frequent unnecessary changes in the topology of an existing SPT and may lead to routing instability. We present new dynamic SPT algorithms that make use of the structure of the previously computed SPT. Besides efficiency, our algorithm design objective is to achieve routing stability by making minimum changes to the topology of an existing SPT (while maintaining shortest path property) when some link states in the network have changed. We establish an algorithmic framework that allows us to characterize a variety of dynamic SPT algorithms including dynamic versions of the well-known Dijkstra, Bellman-Ford, D'Esopo-Pape algorithms, and to establish proofs of correctness for these algorithms in a unified way. The theoretical asymptotic complexity of our new dynamic algorithms matches the best known results in the literature     

Optimal mapping of virtual networks with hidden hops

Network virtualization has emerged as a solution for the Internet inability to address the required challenges caused by the lack of coordination among Internet service providers for the deployment of new services. The allocation of resources is one of the main problems in network virtualization, mainly in the mapping of virtual nodes and links to specific substrate nodes and paths, also known as the virtual network embedding problem. This paper proposes an algorithm based on optimization theory, to map the virtual links and nodes requiring a specific demand, looking for the maximization of the spare bandwidth and spare CPU in the substrate network, taking into account the CPU demanded by the hidden hops when a virtual link is mapped. The components of the virtual networks (nodes and links) that do not ask for an specific demand are then allocated following a fairness criteria.     

Routing in ad hoc networks: a case for long hops

For multihop wireless networks, a fundamental question is whether it is advantageous to route over many short hops (short-hop routing) or over a smaller number of longer hops (long-hop routing). Short-hop routing has gained a lot of support, and its proponents mainly produce two arguments: reduced energy consumption and higher signal-to-interference ratios. Both arguments stem from a simplified analysis based on crude channel models that neglects delay, end-to-end reliability, bias power consumption, the impact of channel coding, mobility, and routing overhead. In this article we shed more light on these issues by listing 18 reasons why short-hop routing is not as beneficial as it seems to be. We also provide experimental evidence to support this claim. The conclusion is that for many networks, long-hop routing is in every aspect a very competitive strategy.