Probability based dynamic-alternate routing and the corresponding converter placement algorithm in all-optical WDM networks

This paper proposes a new dynamic-alternate routing algorithm and its corresponding converter placement algorithm in order to reduce the connection blocking probability for all-optical WDM networks. The main idea in the proposed dynamic-alternate routing algorithm is to try to route the traffics according to a predefined optimal probability distribution. The problem for finding the optimal probability distribution was shown as a convex optimization problem. The problem can be solved by flow deviation method or other standard optimization techniques. Simulation results show that the proposed routing algorithm yields lower connection blocking probabilities than the previous works. The proposed routing algorithm produces similar traffic pattern as the optimal traffic pattern. The similarity between the traffic pattern produced by the proposed dynamic-alternate routing algorithm and the optimal traffic pattern can be further employed for solving other network designing problems such as converter placement problem. Since the optimal traffic pattern can be easily predicted, the optimal traffic pattern which minimizes the blocked traffic intensity is utilized for finding the locations of wavelength converters. The key idea is to place the wavelength converters at the nodes where they are needed most. Simulations have been performed to study the performance of the proposed wavelength converter placement method. The simulation results have shown that the proposed placement method combined with the proposed probability based dynamic-alternate routing algorithm yields smaller connection blocking probability than the two converter placement methods with their corresponding alternate routing algorithms.     

Combining VNS with Genetic Algorithm to solve the one-to-one routing issue in road networks

Computing the optimal route to go from one place to another is a highly important issue in road networks. The problem consists of finding the path that minimizes a metric such as distance, time, cost etc. to go from one node to another in a directed or undirected graph. Although standard algorithms such as Dijkstra are capable of computing shortest paths in polynomial times, they become very slow when the network becomes very large. Furthermore, traditional methods are incapable of meeting additional constraints that may arise during routing in transportation systems such as computing multi-objective routes, routing in stochastic networks. Therefore, we have thought about using meta-heuristics to solve the routing issue in road networks. Meta-heuristics are capable of copying with additional constraints and providing optimal or near optimal routes within reasonable computational times even in large-scale networks. The proposed approach is based on a hybridization process done between a Genetic Algorithm (GA) that belongs to the population-based metaheuristics and a variable neighborhood search (VNS) that performs with one single solution. To evaluate our method, we made experimentations using random generated and real road network instances. We compare our approach with two exact algorithms (Dijkstra and Integer Programming) as well as with GA and VNS when they are executed solely. Experimental results have proven the efficiency of our approach in comparison with the other approaches.     

An algorithmic study of switch graphs

We derive a variety of results on the algorithmics of switch graphs. On the negative side we prove hardness of the following problems: Given a switch graph, does it possess a bipartite/planar/triangle-free/Eulerian configuration? On the positive side we design fast algorithms for several connectivity problems in undirected switch graphs, and for recognizing acyclic configurations in directed switch graphs.     

A heuristic for placement of limited range wavelength converters in all-optical networks

Wavelength routed optical networks have emerged as a technology that can effectively utilize the enormous bandwidth of the optical fiber. Wavelength converters play an important role in enhancing the fiber utilization and reducing the overall call blocking probability of the network. As the distortion of the optical signal increases with the increase in the range of wavelength conversion in optical wavelength converters, limited range wavelength conversion assumes importance. Placement of wavelength converters is a NP complete problem [K.C. Lee, V.O.K. Li, IEEE J. Lightwave Technol. 11 (1993) 962–970] in an arbitrary mesh network. In this paper, we investigate heuristics for placing limited range wavelength converters in arbitrary mesh wavelength routed optical networks. The objective is to achieve near optimal placement of limited range wavelength converters resulting in reduced blocking probabilities and low distortion of the optical signal. The proposed heuristic is to place limited range wavelength converters at the most congested nodes, nodes which lie on the long lightpaths and nodes where conversion of optical signals is significantly high. We observe that limited range converters at few nodes can provide almost the entire improvement in the blocking probability as the full range wavelength converters placed at all the nodes. Congestion control in the network is brought about by dynamically adjusting the weights of the channels in the link thereby balancing the load and reducing the average delay of the traffic in the entire network. Simulations have been carried out on a 12-node ring network, 14-node NSFNET, 19-node European Optical Network (EON), 28-node US long haul network, hypothetical 30-node INET network and the results agree with the analysis.     

Routing and wavelength assignment for hypercube communications embedded on optical chordal ring networks of degrees 3 and 4

Routing and wavelength assignment for realizing hypercube communications on WDM ring networks has been discussed in previous research. To reduce the wavelength requirement, we study routing and wavelength assignment for realizing hypercube communications on WDM ring networks with additional links. We design the embedding schemes and derive the numbers of wavelengths required on WDM chordal ring networks of both degrees 3 and 4. Based on our proposed embedding schemes, we provide the analysis of chord length with optimal number of wavelengths to realize hypercube communications on 3-degree and 4-degree chordal rings. Results show that the wavelength requirement for realizing hypercube communications on optical chordal ring networks is significantly lower than that on optical ring networks. In addition, our research also provides solutions for embedding hypercube graph on chordal rings in graph embedding theory.     

Traffic grooming, routing, and wavelength assignment in WDM transport networks with sparse grooming resources

While a single fiber strand in wavelength division multiplexing (WDM) has over a terabit-per-second bandwidth and a wavelength channel has over a gigabit-per-second transmission speed, the network may still be required to support traffic requests at rates that are lower than the full wavelength capacity. To avoid assigning an entire lightpath to a small request, many researchers have looked at adding traffic grooming to the routing and wavelength assignment (RWA) problem. In this work, we consider the RWA problem with traffic grooming (GRWA) for mesh networks under static and dynamic lightpath connection requests. The GRWA problem is NP-Complete since it is a generalization of the RWA problem which is known to be NP-Complete. We propose an integer linear programming (ILP) model that accurately depicts the GRWA problem. Because it is very hard to find a solution for large networks using ILP, we solve the GRWA problem by proposing two novel heuristics. The strength of the proposed heuristics stems from their simplicity, efficiency, and applicability to large-scale networks. Our simulation results demonstrate that deploying traffic grooming resources on the edge of optical networks is more cost effective and results in a similar blocking performance to that obtained when distributing the grooming resources throughout the optical network domain.     

Minimum cost service composition in service overlay networks

In service computing, it is often desirable to find the service composition solution for a given service composition request such that the total cost of the service composition solution is minimized. In this paper, we study the problem of finding the minimum cost service composition (MCSC) for a general service composition request which is represented by a directed acyclic graph (DAG). We first prove that the general case of the MCSC problem is NP-Hard. We then show that optimal solutions can be found in polynomial time for some special structured service composition requests. To this end, we derive a sufficient condition on the service composition request graph and propose corresponding algorithms to find the optimal solutions in polynomial time. Using such algorithms as building blocks, we propose heuristic algorithms to decompose the general service composition request graph into service composition request subgraphs with optimal structures. Simulation results demonstrate the effectiveness of the proposed heuristic algorithms.     

Resource finding in store-and-forward networks

We present a model of searching for a resource in a distributed system whose nodes are connected through a store-and-forward network. Based on this model, we show a lower bound on the number of messages needed to find a resource when nothing is known about the nodes that have the current location of the resource. The model also helps us to establish results about the time complexity of determining a message optimal resource finding algorithm when the probability distribution for the location of the resource in the network is known. We show that the optimization problem is NP-hard for general networks. Finally we show that optimal resource finding algorithms can be determined in polynomial time for a class of tree networks and bidirectional rings. The polynomial algorithms can be used as a basis of heuristic algorithms for general networks.This work was supported in part by NSF grants CCR-8806358 and NCR-8604850     

Designing robust network topologies for wireless sensor networks in adversarial environments

In this paper, we address the problem of deploying sink nodes in a wireless sensor network such that the resulting network topology be robust. In order to measure network robustness, we propose a new metric, called persistence, which better captures the notion of robustness than the widely known connectivity based metrics. We study two variants of the sink deployment problem: sink selection and sink placement. We prove that both problems are NP-hard, and show how the problem of sink placement can be traced back to the problem of sink selection using an optimal search space reduction technique, which may be of independent interest. To solve the problem of sink selection, we propose efficient heuristic algorithms. Finally, we provide experimental results on the performance of our proposed algorithms.     

光网络中波长转换器的优化放置问题求解

基于分层图模型,提出了一种的简化的计算具有波长转换器光网络中光链路阻塞率的数学模型和公式,并应用于遗传算法的迭代函数,通过遗传算法对波长转换器在光网络中的优化放置问题进行求解,分析了波长转换器的最优放置和波长转换器的最小使用数量。通过在美国自然科学基金网(NSFNet)的仿真模拟,得出了使用部分和全部波长转换时的网络阻塞特性。     

Approximating Node Connectivity Problems via Set Covers

Given a graph (directed or undirected) with costs on the edges, and an integer $k$, we consider the problem of finding a $k$-node connected spanning subgraph of minimum cost. For the general instance of the problem (directed or undirected), there is a simple $2k$-approximation algorithm. Better algorithms are known for various ranges of $n,k$. For undirected graphs with metric costs Khuller and Raghavachari gave a $( 2+{2(k-1)}/{n})$-approximation algorithm. We obtain the following results: (i) For arbitrary costs, a $k$-approximation algorithm for undirected graphs and a $(k+1)$-approximation algorithm for directed graphs. (ii) For metric costs, a $(2+({k-1})/{n})$-approximation algorithm for undirected graphs and a $(2+{k}/{n})$-approximation algorithm for directed graphs. For undirected graphs and $k=6,7$, we further improve the approximation ratio from $k$ to $\lceil (k+1)/2 \rceil=4$; previously, $\lceil (k+1)/2 \rceil$-approximation algorithms were known only for $k \leq 5$. We also give a fast $3$-approximation algorithm for $k=4$. The multiroot problem generalizes the min-cost $k$-connected subgraph problem. In the multiroot problem, requirements $k_u$ for every node $u$ are given, and the aim is to find a minimum-cost subgraph that contains $\max\{k_u,k_v\}$ internally disjoint paths between every pair of nodes $u,v$. For the general instance of the problem, the best known algorithm has approximation ratio $2k$, where $k=\max k_u$. For metric costs there is a 3-approximation algorithm. We consider the case of metric costs, and, using our techniques, improve for $k \leq 7$ the approximation guarantee from $3$ to $2+{\lfloor (k-1)/2 \rfloor}/{k} < 2.5$.     

Lower bounds for the mixed capacitated arc routing problem

Capacitated arc routing problems (CARP) arise in distribution or collecting problems where activities are performed by vehicles, with limited capacity, and are continuously distributed along some pre-defined links of a network. The CARP is defined either as an undirected problem or as a directed problem depending on whether the required links are undirected or directed. The mixed capacitated arc routing problem (MCARP) models a more realistic scenario since it considers directed as well as undirected required links in the associated network. We present a compact flow based model for the MCARP. Due to its large number of variables and constraints, we have created an aggregated version of the original model. Although this model is no longer valid, we show that it provides the same linear programming bound than the original model. Different sets of valid inequalities are also derived. The quality of the models is tested on benchmark instances with quite promising results.     

Robust controllability assessment via semi-definite programming

This paper presents a new framework for systematic assessment of the controllability of uncertain linear time-invariant (LTI) systems. The objective is to evaluate controllability of an uncertain system with norm-bounded perturbation over the entire uncertain region. The method is based on a singular-value minimization problem, over the entire complex plane. To solve the problem, first, a necessary and sufficient condition is proposed to avert the difficulties of griding over the complex plane, and to verify the controllability of directed and undirected networks in a single step. Secondly, the results are utilized to formulate the problem as two Lyapunov-based linear matrix inequalities (LMIs) for undirected networks, and four LMIs, for directed ones. The proposed approach is subsequently extended to evaluate the maximum guaranteed distance to uncontrollability of a system through a quasi-convex optimization problem whose solution is guaranteed to be globally optimal. By duality, analogous results are established for robust observability of directed and undirected networks. The proposed framework is implemented efficiently using LMI tools, and provides a fast and reliable tool for the assessment of robust controllability (and by duality, robust observability). It is also extendable to robust control system design problems such as control node selection for uncertain systems.     

WSM: a novel algorithm for subgraph matching in large weighted graphs

Given an undirected/directed large weighted data graph and a similar smaller weighted pattern graph, the problem of weighted subgraph matching is to find a mapping of the nodes in the pattern graph to a subset of nodes in the data graph such that the sum of edge weight differences is minimum. Biological interaction networks such as protein-protein interaction networks and molecular pathways are often modeled as weighted graphs in order to account for the high false positive rate occurring intrinsically during the detection process of the interactions. Nonetheless, complex biological problems such as disease gene prioritization and conserved phylogenetic tree construction largely depend on the similarity calculation among the networks. Although several existing methods provide efficient methods for graph and subgraph similarity measurement, they produce nonintuitive results due to the underlying unweighted graph model assumption. Moreover, very few algorithms exist for weighted graph matching that are applicable with the restriction that the data and pattern graph sizes are equal. In this paper, we introduce a novel algorithm for weighted subgraph matching which can effectively be applied to directed/undirected weighted subgraph matching. Experimental results demonstrate the superiority and relative scalability of the algorithm over available state of the art methods.     

A consensus graph clustering algorithm for directed networks

Finding groups of highly related vertices in undirected graphs has been widely investigated. Nevertheless, a very few strategies are specially designed for dealing with directed networks. In particular, strategies based on the maximization of the modularity adjusted to overcome the resolution limit for directed networks have not been developed. The analysis of the characteristics of the clusters produced by these approaches is highly important since among the most used strategies for detecting communities in directed networks are the modularity maximization-based algorithms for undirected graphs. Towards these remarks, in this paper we propose a consensus-based strategy, named ConClus, for providing partitions for directed networks guided by the adjusted modularity measure. In the computational experiments, we compared ConClus with benchmark strategies, including Infomap and OSLOM, by using hundreds of LFR networks. ConClus outperformed Infomap and was competitive with OSLOM even for graphs with high mixture index and small-sized clusters, to which modularity-based algorithms have limitations. ConClus outperformed all algorithms when considering the networks with the highest average and maximum in-degrees among the networks used in the experiments.     

Optimal scheduling algorithms in WDM optical interconnects with limited range wavelength conversion capability

Optical communication is a promising candidate for many emerging networking and parallel/distributed computing applications because of its huge bandwidth. Wavelength division multiplexing (WDM) is a technique that can better utilize the optical bandwidth by dividing the bandwidth of a fiber into multiple wavelength channels. In this paper, we study optimal scheduling algorithms to resolve output contentions in bufferless time slotted WDM optical interconnects with wavelength conversion ability. We consider the general case of limited range wavelength conversion with arbitrary conversion capability, as limited range wavelength conversion is easier to implement and more cost effective than full range wavelength conversion, and it also includes full range wavelength conversion as a special case. We first consider the conversion scheme in which each wavelength can be converted to multiple wavelengths in an interval of wavelengths and the intervals for different wavelengths are "ordered". We show that the problem of maximizing network throughput can be formalized as finding a maximum matching in a bipartite graph. We then give an optimal scheduling algorithm called the first available algorithm that runs in O(k) time, where k is the number of wavelengths per fiber. We also study the case where the connection requests have different priorities. We formalize the problem as finding an optimal matching in a weighted bipartite graph and give a scheduling algorithm called the downwards expanding algorithm that runs in O(kD + Nklog(Nk)) time where N is the number of input fibers of the interconnect and D is the conversion degree. Finally, we consider the circular symmetrical wavelength conversion scheme and give optimal scheduling algorithms for nonprioritized scheduling in O(Dk) time and prioritized scheduling in O(k/sup 2/+Nklog(Nk)) time.     

基于三元组结构的有向网链路预测方法

当前链路预测的研究主要集中在无向网络,然而现实世界中存在大量的有向网络,忽略链路的方向会缺失一些重要信息甚至使预测失去意义,而直接将无向网络的预测方法应用于有向网络又存在预测精度降低的问题。为此,提出了一个基于三元组的有向网络链路预测算法,该算法针对有向网络和无向网络三元组结构的不同,应用势理论对三元组进行筛选,通过统计分析不同三元组闭合的可能性,以网络整体三元组闭合指数作为权重计算节点间的相似性。在9个真实数据集上的实验表明,所提方法比基准方法的预测精度提高了4.3%。     

Contention-aware data caching in wireless multi-hop ad hoc networks

This paper studies a challenging problem of cache placement in wireless multi-hop ad hoc networks. More specifically, we study how to achieve an optimal tradeoff between total access delay and caching overheads, by properly selecting a subset of wireless nodes as cache nodes when the network topology changes. We assume a data source updates a data item to be accessed by other client nodes. Most of the existing cache placement algorithms use hop counts to measure the total cost of a caching system, but hop delay in wireless networks varies much due to the contentions among these nodes and the traffic load on each link. Therefore, we evaluate the per-hop delay for each link according to the contentions detected by a wireless node from the MAC layer. We propose two heuristic cache placement algorithms, named Centralized Contention-aware Caching Algorithm (CCCA) and Distributed Contention-aware Caching Algorithm (DCCA), both of which detect the variation of contentions and the change of the traffic flows, in order to evaluate the benefit of selecting a node as a cache node. We also apply a TTL-based cache consistency strategy to maintain the delta consistency among all the cache nodes. Simulation results show that the proposed algorithms achieve better performance than other alternative ones in terms of average query delay, caching overheads, and query success ratio.     

Community discovery using nonnegative matrix factorization

Complex networks exist in a wide range of real world systems, such as social networks, technological networks, and biological networks. During the last decades, many researchers have concentrated on exploring some common things contained in those large networks include the small-world property, power-law degree distributions, and network connectivity. In this paper, we will investigate another important issue, community discovery, in network analysis. We choose Nonnegative Matrix Factorization (NMF) as our tool to find the communities because of its powerful interpretability and close relationship between clustering methods. Targeting different types of networks (undirected, directed and compound), we propose three NMF techniques (Symmetric NMF, Asymmetric NMF and Joint NMF). The correctness and convergence properties of those algorithms are also studied. Finally the experiments on real world networks are presented to show the effectiveness of the proposed methods.     

Letter to the editor

The maximal-cut problem for directed graphs can be defined analogously to that for the undirected case. The undirected problem is known to be NP-complete. We consider two directed variants of the problem. Depending on the definition of the value of a cut, the resulting problem for general directed graphs is either efficiently solvable or NP-complete. We show that the latter version of the problem remains NP-complete when restricted to acyclic directed graphs. Further restriction to directed trees yields an efficiently solvable problem. We present an algorithm solving the problem in time proportional to the size of the input.