Packet Routing and PRAM Emulation on Star Graphs and Leveled Networks

We consider the problem of permutation routing on a star graph, an interconnection network which has better properties than the hypercube. In particular, its degree and diameter are sublogarithmic in the network size. We present optimal randomized routing algorithms that run in O(D) steps (where D is the network diameter) for the worst-case input with high probability. We also show that for the n-way shuffle network with N = nⁿ nodes, there exists a randomized routing algorithm which runs in O(n) time with high probability. Another contribution of this paper is a universal randomized routing algorithm that could do optimal routing for a large class of networks (called leveled networks) which includes the star graph. The associative analysis is also network-independent. In addition, we present a deterministic routing algorithm, for the star graph, which is near optimal. All the algorithms we give are oblivious. As an application of our routing algorithms, we also show how to emulate a PRAM optimally on this class of networks.     

Energetic sustainability of routing algorithms for energy-harvesting wireless sensor networks

A new class of wireless sensor networks that harvest power from the environment is emerging because of its intrinsic capability of providing unbounded lifetime. While a lot of research has been focused on energy-aware routing schemes tailored to battery-operated networks, the problem of optimal routing for energy harvesting wireless sensor networks (EH-WSNs) has never been explored. The objective of routing optimization in this context is not extending network lifetime, but maximizing the workload that can be autonomously sustained by the network.In this work we present a methodology for assessing the energy efficiency of routing algorithms for networks whose nodes drain power from the environment. We first introduce the energetic sustainability problem, then we define the maximum energetically sustainable workload (MESW) as the objective function to be used to drive the optimization of routing algorithms for EH-WSNs.We propose a methodology that makes use of graph algorithms and network simulations for evaluating the MESW starting from a network topology, a routing algorithm and a distribution of the environmental power available at each node. We present a tool flow implementing the proposed methodology and we show comparative results achieved on several routing algorithms.Experimental results highlight that routing strategies that do not take into account environmental power do not provide optimal results in terms of workload sustainability. Using optimal routing algorithms may lead to sizeable enhancements of the maximum sustainable workload. Moreover, optimality strongly depends on environmental power configurations. Since environmental power sources change over time, our results prompt for a new class of routing algorithms for EH-WSNs that are able to dynamically adapt to time-varying environmental conditions.     

Extracting certainty from uncertainty: regret bounded by variation in costs

Prediction from expert advice is a fundamental problem in machine learning. A major pillar of the field is the existence of learning algorithms whose average loss approaches that of the best expert in hindsight (in other words, whose average regret approaches zero). Traditionally the regret of online algorithms was bounded in terms of the number of prediction rounds. Cesa-Bianchi, Mansour and Stoltz (Mach. Learn. 66(2–3):21–352, 2007) posed the question whether it is be possible to bound the regret of an online algorithm by the variation of the observed costs. In this paper we resolve this question, and prove such bounds in the fully adversarial setting, in two important online learning scenarios: prediction from expert advice, and online linear optimization.     

A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs

This work deals with a class of problems under interval data uncertainty, namely interval robust-hard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-of-the-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems.     

A survey of routing algorithm for mesh Network-on-Chip

With the rapid development of semiconductor industry, the number of cores integrated on chip increases quickly, which brings tough challenges such as bandwidth, scalability and power into on-chip interconnection. Under such background, Network-on-Chip (NoC) is proposed and gradually replacing the traditional on-chip interconnections such as sharing bus and crossbar. For the convenience of physical layout, mesh is the most used topology in NoC design. Routing algorithm, which decides the paths of packets, has significant impact on the latency and throughput of network. Thus routing algorithm plays a vital role in a wellperformed network. This study mainly focuses on the routing algorithms of mesh NoC. By whether taking network information into consideration in routing decision, routing algorithms of NoC can be roughly classified into oblivious routing and adaptive routing. Oblivious routing costs less without adaptiveness while adaptive routing is on the contrary. To combine the advantages of oblivious and adaptive routing algorithm, half-adaptive algorithms were proposed. In this paper, the concepts, taxonomy and features of routing algorithms of NoC are introduced. Then the importance of routing algorithms in mesh NoC is highlighted, and representative routing algorithms with respective features are reviewed and summarized. Finally, we try to shed light upon the future work of NoC routing algorithms.     

A note on the k-Canadian Traveller Problem

We consider the online problem k-CTP, which is the problem to guide a vehicle from some site s to some site t on a road map given by a graph G=(V,E) in which up to k (unknown) edges are blocked by avalanches. An online algorithm learns from a blocked edge when reaching one of its endpoints. Thus, it might have to change its route to the target t up to k times. We show that no deterministic online algorithm can achieve a competitive ratio smaller than 2k+1 and give an easy algorithm which matches this lower bound. Furthermore, we show that randomization can not improve the competitive ratio substantially, by establishing a lower bound of k+1 for the competitivity of randomized online algorithms against an oblivious adversary.     

Regret bounded by gradual variation for online convex optimization

Recently, it has been shown that the regret of the Follow the Regularized Leader (FTRL) algorithm for online linear optimization can be bounded by the total variation of the cost vectors rather than the number of rounds. In this paper, we extend this result to general online convex optimization. In particular, this resolves an open problem that has been posed in a number of recent papers. We first analyze the limitations of the FTRL algorithm as proposed by Hazan and Kale (in Machine Learning 80(2–3), 165–188, 2010) when applied to online convex optimization, and extend the definition of variation to a gradual variation which is shown to be a lower bound of the total variation. We then present two novel algorithms that bound the regret by the gradual variation of cost functions. Unlike previous approaches that maintain a single sequence of solutions, the proposed algorithms maintain two sequences of solutions that make it possible to achieve a variation-based regret bound for online convex optimization. To establish the main results, we discuss a lower bound for FTRL that maintains only one sequence of solutions, and a necessary condition on smoothness of the cost functions for obtaining a gradual variation bound. We extend the main results three-fold: (i) we present a general method to obtain a gradual variation bound measured by general norm; (ii) we extend algorithms to a class of online non-smooth optimization with gradual variation bound; and (iii) we develop a deterministic algorithm for online bandit optimization in multipoint bandit setting.     

Design and performance analysis of an inductive QoS routing algorithm

Routing mechanism is key to the success of large-scale, distributed communication and heterogeneous networks. Consequently, computing constrained shortest paths is fundamental to some important network functions such as QoS routing and traffic engineering. The problem of QoS routing with multiple additive constraints is known to be NP-complete but researchers have been designing heuristics and approximation algorithms for multi-constrained paths algorithms to propose pseudo-polynomial time algorithms. This paper introduces a polynomial time approximation quality of service (QoS) routing algorithm and constructs dynamic state-dependent routing policies. The proposed algorithm uses an inductive approach based on trial/error paradigm combined with swarm adaptive approaches to optimize lexicographically various QoS criteria. The originality of our approach is based on the fact that our system is capable to take into account the dynamics of the network where no model of the network dynamics is assumed initially. Our approach samples, estimates, and builds the model of pertinent aspects of the environment which is very important in heterogeneous networks. The algorithm uses a model that combines both a stochastic planned pre-navigation for the exploration phase and a deterministic approach for the backward phase. Multiple paths are searched in parallel to find the K best qualified ones. To improve the overall network performance, a load adaptive balancing policy is defined and depends on a dynamic traffic path probability distribution function. We conducted a performance analysis of the proposed QoS routing algorithm using OPNET based on a platform simulated network. The obtained results demonstrate substantial performance improvements as well as the benefits of learning approaches over networks with dynamically changing traffic.     

Complexity and design of QoS routing algorithms in wireless mesh networks

Quality of service (QoS) provisioning in wireless mesh networks (WMNs) is an open issue to support emerging multimedia services. In this paper, we study the problem of QoS provisioning in terms of end-to-end bandwidth allocation in WMNs. It is challenging due to interferences in the networks. We consider widely used interference models and show that except a few special cases, the problem of finding a feasible path is NP-complete under the models. We propose a k-shortest path based algorithmic framework to solve this problem. We also consider the problem of optimizing network performance by on-line dynamic routing, and adapt commonly used conventional QoS routing metrics to be used in WMNs. We find the optimal solutions for these problems through formulating them as optimization models. A model is developed to check the existence of a feasible path and another to find the optimal path for a demand; moreover, an on-line optimal QoS routing algorithm is developed. Comparing the algorithms implemented by the proposed framework with the optimization models shows that our solution can find existing feasible paths with high probability, efficiently optimizes path lengths, and has a comparable performance to the optimal QoS routing algorithm. Furthermore, our results show that contrary to wireline networks, minimizing resource consumption should be preferred over load distribution even in lightly loaded WMNs.     

Dynamic load balancing in IP-over-WDM optical burst switching networks

In this paper, we consider the problem of dynamic load balancing in wavelength division multiplexing (WDM)-based optical burst switching (OBS) networks. We propose a load balancing scheme based on adaptive alternate routing aimed at reducing burst loss. The key idea of adaptive alternate routing is to reduce network congestion by adaptively distributing the load between two pre-determined link-disjoint alternative paths based on the measurement of the impact of traffic load on each of them. We develop two alternative-path selection schemes to select link-disjoint alternative paths to be used by adaptive alternate routing. The path selection schemes differ in the way the cost of a path is defined and in the assumption made about the knowledge of the traffic demands. Through extensive simulation experiments for different traffic scenarios, we show that the proposed dynamic load balancing algorithm outperforms the shortest path routing and static alternate routing algorithms.     

Decremental algorithm for adaptive routing incorporating traveler information

Routing in a stochastic and dynamic (time-dependent) network is a crucial transportation problem. A new variant of adaptive routing, which assumes perfect online information of continuous real-time link travel time, is proposed. Driver's speed profile is taken into consideration to realistically estimate travel times, which also involves the stochasticity of links in a dynamic network. An adaptive approach is suggested to tackle the continuous dynamic shortest path problem. A decremental algorithm is consequently developed to reduce optimization time. The impact of the proposed adaptive routing and the performance of the decremental approach are evaluated in static and dynamic networks under different traffic conditions. The proposed approach can be incorporated into vehicle navigation systems.     

一种QoS平面蚁群路由算法的设计与实现

提高网络服务质量的关键在于寻找出高性能路由,然而传统的路由算法却很难解决此类NP C问题。基于此,本文提出一种基于改进后的自适应蚁群算法的路由解决方案,将路由问题假设为平面路由,并建立相应的网络模型。针对该网络模型,建立特定的平面QoS蚁群路由算法,并在MATLAB上对其进行模拟仿真,从而验证了它的性能。仿真实验结果表明,该路由选择方案在求解实际网络路由问题时具有一定的优越性,能够有效地解决QoS平面网络路由问题。     

New lower bounds for online k-server routing problems

In a k-server routing problem k?1 servers move in a metric space in order to visit specified points or carry objects from sources to destinations. In the online version requests arrive online while the servers are traveling. Two classical objective functions are to minimize the makespan, i.e., the time when the last server has completed its tour (k-Traveling Salesman Problem or k-tsp) and to minimize the sum of completion times (k-Traveling Repairman Problem or k-trp). Both problems, the k-tsp and the k-trp have been studied from a competitive analysis point of view, where the cost of an online algorithm is compared to that of an optimal offline algorithm. However, the gap between the obtained competitive ratios and the corresponding lower bounds have mostly been quite large for k>1, in particular for randomized algorithms against an oblivious adversary.We reduce a number of gaps by providing new lower bounds for randomized algorithms. The most dramatic improvement is in the lower bound for the k-Dial-a-Ride-Problem (the k-trp when objects need to be carried) from to 3 which is currently also the best lower bound for deterministic algorithms.     

Adaptive deadlock- and livelock-free routing in the hypercubenetwork

This paper consists of two parts. In the first one, two new algorithms for wormhole routing on the hypercube network are presented. These techniques are adaptive and are ensured to be deadlock- and livelock-free. These properties are guaranteed by using a small number of resources in the routing node. The first algorithm is adaptive and nonminimal and will be referred to as Nonminimal. In this technique, some moderate derouting is allowed in order to alleviate the potential congestion arising from highly structured communication patterns. The second algorithm, dubbed Subcubes, is adaptive and minimal, and is based on partitioning the hypercube into subcubes of smaller dimension; This technique requires only two virtual channels per physical link of the node. In the second part of the paper, a wide variety of techniques for wormhole routing in the hypercube are evaluated from an algorithmic point of view. Five partially adaptive algorithms are considered: the Hanging algorithm, the Zenith algorithm, the Hanging-Order algorithm, the Nonminimal algorithm; and the Subcubes algorithm. One oblivious algorithm, the Dimension-Order, or E-Cube routing algorithm, is also used. Finally, a Fully Adaptive Minimal algorithm is tried. A simple node model was designed and adapted to all the algorithms     

Fault-tolerant wormhole routing for hypercube networks

We present an adaptive fault-tolerant wormhole routing algorithm for hypercubes by using 3 virtual networks. The routing algorithm can tolerate at least n−1 faulty nodes and can route a message via a path of length no more than the shortest path plus four. Previous algorithms which achieve the same fault tolerant ability need 5 virtual networks. Simulation results are also given in this paper.     

Adaptive Routing on the New Switch Chip for IBM SP Systems

The IBM RS/6000 SP is one of the most successful commercially available multicomputers. SP owes its success partially to the scalable, high bandwidth, low latency network. This paper describes the architecture of Switch2 switch chip, the recently developed third generation switching element which future IBM RS/6000 SP systems may be based on. Switch2 offers significant enhancements over the existing SP switch chips by incorporating advances in both VLSI technology and interconnection network research. One of the major new features of Switch2 is the incorporation of adaptive routing support into it. We describe the adaptive source routing architecture of the Switch2 chip which is a unique feature of this chip. The performance of the adaptive source routing and oblivious routing for a wide range of system characteristics and traffic patterns is evaluated. It is shown that adaptive source routing outperforms or performs comparably with oblivious routing. We propose two novel algorithms for generating adaptive routes specifications required for enabling the usage of adaptive source routing. A comparison between the cost of these two algorithms and the performance improvement obtained from using these algorithms are discussed. We also propose different output selection functions to be used in switching elements for implementing the adaptive routing. We evaluate and compare the performance of these selection functions and discover that the best selection functions for BMINs are not dependent on the traffic pattern, message size, or system size.     

一种带约束的多目标服务质量路由算法

多约束服务质量(QoS)路由是要求在多个约束条件下计算满足所有独立限制条件的可行路径．将这种NPC问题转化为一种带约束条件的多目标优化问题，根据多目标遗传算法的智能优化原理，提出一种多目标QoS路由算法来产生一组最优非劣路由．理论分析和实验结果表明，使用带约束的多目标遗传算法是解决多约束QoS路由的有效途径，能对提高网络性能起到重要作用．     

无线传感器网络中能量有效自适应路由算法研究

针对无线传感器网络寿命最大化问题,基于无线传感器节点能耗分布特点和数据传输能耗模型,建立无线传感器网络生存周期的数学优化模型,并针对最小能耗路由的能耗不均衡问题和能量均衡路由的能耗开销问题,综合考虑网络中节点的剩余能量和节点间发送数据的能耗,提出一个适合无线多跳传感器网络的自适应路由算法。仿真结果表明,提出的路由算法能充分地利用有限的能量资源,较大地延长网络生存周期。     

无线传感器网络中能量有效自适应路由算法研究

针对无线传感器网络寿命最大化问题,基于无线传感器节点能耗分布特点和数据传输能耗模型,建立无线传感器网络生存周期的数学优化模型,并针对最小能耗路由的能耗不均衡问题和能量均衡路由的能耗开销问题,综合考虑网络中节点的剩余能量和节点间发送数据的能耗,提出一个适合无线多跳传感器网络的自适应路由算法。仿真结果表明,提出的路由算法能充分地利用有限的能量资源,较大地延长网络生存周期。