<Emphasis Type="Italic">p</Emphasis>-RWBO: a novel low-collision and QoS-supported MAC for wireless ad hoc networks

QoS supported MAC mechanism is a key issue for supporting QoS in wireless ad hoc networks. A new backoff algorithm, named RWBO＋BEB, was proposed previ- ously to decrease the packet collision probability significantly. In this paper, it is explored how to make RWBO＋BEB support service differentiation in wireless ad hoc networks, and a novel proportional service differentiation algorithm, named p-RWBO, is proposed to allocate the wireless bandwidth according to the band- width ratio of each station. In p-RWBO, station n＇s walking probability （Pw,n） is selected according to its allocated bandwidth ratio. An analytical model is proposed to analyze how to choose Pw, n according to the bandwidth ratios of station n. The simulation results indicate that p-RWBO can differentiate services in terms of both bandwidth and delay.     

Many-to-Many Communication in Radio Networks

Radio networks model wireless data communication when the bandwidth is limited to one wave frequency. The key restriction of such networks is mutual interference of packets arriving simultaneously at a node. The many-to-many (m2m) communication primitive involves p participant nodes from among n nodes in the network, where the distance between any pair of participants is at most d. The task is to have all the participants get to know all the input messages. We consider three cases of the m2m communication problem. In the ad-hoc case, each participant knows only its name and the values of n, p and d. In the partially centralized case, each participant knows the topology of the network and the values of p and d, but does not know the names of the other participants. In the centralized case, each participant knows the topology of the network and the names of all the participants. For the centralized m2m problem, we give deterministic protocols, for both undirected and directed networks, working in time, which is provably optimal. For the partially centralized m2m problem, we give a randomized protocol for undirected networks working in time with high probability (whp), and we show that any deterministic protocol requires time. For the ad-hoc m2m problem, we develop a randomized protocol for undirected networks that works in time whp. We show two lower bounds for the ad-hoc m2m problem. One lower bound states that any randomized protocol for the m2m ad hoc problem requires expected time. Another lower bound states that for any deterministic protocol for the m2m ad hoc problem, there is a network on which the protocol requires time when n−p(n)=Ω(n) and d>1, and that it requires Ω(n) time when n−p(n)=o(n). The results of this paper appeared in a preliminary form in “On many-to-many communication in packet radio networks” in Proceedings of the 10th Conference on Principles of Distributed Systems (OPODIS), Bordeaux, France, 2006, Lecture Notes in Computer Science 4305, Springer, Heidelberg, pp. 258–272. The work of B.S. Chlebus was supported by NSF Grant 0310503.     

Random walks for selected boolean implication and equivalence problems

This paper is concerned with the design and analysis of a random walk algorithm for the 2CNF implication problem (2CNFI). In 2CNFI, we are given two 2CNF formulas f₁{\phi_{1}} and f₂{\phi_{2}} and the goal is to determine whether every assignment that satisfies f₁{\phi_{1}} , also satisfies f₂{\phi_{2}} . The implication problem is clearly coNP-complete for instances of kCNF, k ≥ 3; however, it can be solved in polynomial time, when k ≤ 2. The goal of this paper is to provide a Monte Carlo algorithm for 2CNFI with a bounded probability of error. The technique developed for 2CNFI is then extended to derive a randomized, polynomial time algorithm for the problem of checking whether a given 2CNF formula Nae-implies another 2CNF formula.     

Globally exponentially attractive sets of the family of Lorenz systems

In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b→ 1^＋ and a→0^＋, for which the previous methods failed, have been solved using a unified formula.     

Attack Propagation in Networks

A new model for intrusion and its propagation through various attack schemes in networks is considered. The model is characterized by the number of network nodes n, and two parameters f and g. Parameter f represents the probability of failure of an attack to a node and is a gross measure of the level of security of the attacked system and perhaps of the intruder’s skills; g represents a limit on the number of attacks that the intrusion software can ever try, due to the danger of being discovered, when it issues them from a particular (broken) network node. The success of the attack scheme is characterized by two factors: the number of nodes captured (the spread factor) and the number of virtual links that a defense mechanism has to trace from any node where the attack is active to the origin of the intrusion (the traceability factor). The goal of an intruder is to maximize both factors. In our model we present four different ways (attack schemes) by which an intruder can organize his attacks. Using analytic and experimental methods, we first show that for any 0 < f < 1, there exists a constant g for which any of our attack schemes can achieve a Θ(n) spread and traceability factor with high probability, given sufficient propagation time. We also show for three of our attack schemes that the spread and the traceability factors are, with high probability, linearly related during the whole duration of the attack propagation. This implies that it will not be easy for a detection mechanism to trace the origin of the intrusion, since it will have to trace a number of links proportional to the nodes captured.     

Approximation Algorithm Based on Chain Implication for Constrained Minimum Vertex Covers in Bipartite Graphs

The constrained minimum vertex cover problem on bipartite graphs (the Min-CVCB problem) is an important NP-complete problem. This paper presents a polynomial time approximation algorithm for the problem based on the technique of chain implication. For any given constant ε > 0, if an instance of the Min-CVCB problem has a minimum vertex cover of size (ku, kl), our algorithm constructs a vertex cover of size (ku*, kl* ), satisfying max{ku*/ku, kl* /kl} 1 ε.     

Shannon capacity in poisson wireless network model

We consider a realistic model of a wireless network where nodes are dispatched in an infinite map with uniform distribution. Signals decay with distance according to attenuation factor α. At any time we assume that the distribution of emitters is λ per square unit area. From an explicit formula of the Laplace transform of a received signal, we derive an explicit formula for the information rate received by an access point at a random position, which is α/2(log 2)⁻¹ per Hertz. We generalize to network maps of any dimension.     

Stackelberg Strategies for Selfish Routing in General Multicommodity Networks

A natural generalization of the selfish routing setting arises when some of the users obey a central coordinating authority, while the rest act selfishly. Such behavior can be modeled by dividing the users into an α fraction that are routed according to the central coordinator’s routing strategy (Stackelberg strategy), and the remaining 1−α that determine their strategy selfishly, given the routing of the coordinated users. One seeks to quantify the resulting price of anarchy, i.e., the ratio of the cost of the worst traffic equilibrium to the system optimum, as a function of α. It is well-known that for α=0 and linear latency functions the price of anarchy is at most 4/3 (J. ACM 49, 236–259, 2002). If α tends to 1, the price of anarchy should also tend to 1 for any reasonable algorithm used by the coordinator. We analyze two such algorithms for Stackelberg routing, LLF and SCALE. For general topology networks, multicommodity users, and linear latency functions, we show a price of anarchy bound for SCALE which decreases from 4/3 to 1 as α increases from 0 to 1, and depends only on α. Up to this work, such a tradeoff was known only for the case of two nodes connected with parallel links (SIAM J. Comput. 33, 332–350, 2004), while for general networks it was not clear whether such a result could be achieved, even in the single-commodity case. We show a weaker bound for LLF and also some extensions to general latency functions. The existence of a central coordinator is a rather strong requirement for a network. We show that we can do away with such a coordinator, as long as we are allowed to impose taxes (tolls) on the edges in order to steer the selfish users towards an improved system cost. As long as there is at least a fraction α of users that pay their taxes, we show the existence of taxes that lead to the simulation of SCALE by the tax-payers. The extension of the results mentioned above quantifies the improvement on the system cost as the number of tax-evaders decreases. Research of G. Karakostas supported by an NSERC Discovery Grant and MITACS. Research of S. Kolliopoulos partially supported by the University of Athens under the project Kapodistrias.     

On the Stability of Dynamic Diffusion Load Balancing

We consider the problem of dynamic load balancing in arbitrary (connected) networks on n nodes. Our load generation model is such that during each round, n tasks are generated on arbitrary nodes, and then (possibly after some balancing) one task is deleted from every non-empty node. Notice that this model fully saturates the resources of the network in the sense that we generate just as many new tasks per round as the network is able to delete. We show that even in this situation the system is stable, in that the total load remains bounded (as a function of n alone) over time. Our proof only requires that the underlying “communication” graph be connected. (It of course also works if we generate less than n new tasks per round, but the major contribution of this paper is the fully saturated case.) We further show that the upper bound we obtain is asymptotically tight (up to a moderate multiplicative constant) by demonstrating a corresponding lower bound on the system load for the particular example of a linear array (or path). We also show some simple negative results (i.e., instability) for work-stealing based diffusion-type algorithms in this setting. A preliminary version of this paper entitled “Dynamic diffusion load balancing” was published in Proc. 32nd International Colloquium on Automata, Languages and Programming (ICALP’05), Lecture Notes in Computer Science 3580, Springer-Verlag, pp. 1386–1398. P. Berenbrink is supported by NSERC Discovery Grant 250284-2002. R. Martin is supported by EPSRC grant “Discontinuous Behaviour in the Complexity of Randomized Algorithms.”     

Blaschke products and optimal recovery inH ∞

We examine the error in the optimal estimation of∫ ₋₁ ¹ f(t)w(t)dt by a quadrature formula using values off at equally spaced points of (−1, 1) or at the zeros of ultraspherical polynomials. Heref is known to be an analytic function in the unit disc which is bounded by l andw is a given weight function with prescribed behavior near ±1. A major role in our investigations is played by bounds on (−1, 1) from above and below for the finite Blaschke product which is based in the nodes of the quadrature formula. Optimal estimation of the functionf, rather than its integral, is also studied.     

Bounded dilation maps of hypercubes into Cayley graphs on the symmetric group

LetG andH be graphs with |V(G)≤ |V(H)|. Iff:V(G) →V(H) is a one-to-one map, we letdilation(f) be the maximum of dist _H (f x),f(y)) over all edgesxy inG where dist _H denotes distance inH. The construction of maps fromG toH of small dilation is motivated by the problem of designing small slowdown simulations onH of algorithms that were originally designed for the networkG. LetS(n), thestar network of dimension n, be the graph whose vertices are the elements of the symmetric group of degreen, two verticesx andy being adjacent ifx o (1,i) =y for somei. That is,xy is an edge ifx andy are related by a transposition involving some fixed symbol (which we take to be 1). Also letP(n), thepancake network of dimension n, be the graph whose vertices are the elements of the symmetric group of degreen, two verticesx andy being adjacent if one can be obtained from the other by reversing some prefix. That is,xy is an edge ifx andy are related byx o (1,i(2,i-1) ⋯ ([i/2], [i/2]) =y. The star network (introduced in [AHK]) has nice symmetry properties, and its degree and diameter are sublogarithmic as functions of the number of vertices, making it compare favorably with the hypercube network. These advantages ofS(n) motivate the study of how well it can simulate other parallel computation networks, in particular, the hypercube. The concern of this paper is to construct low dilation maps of hypercube networks into star or pancake networks. Typically in such problems, there is a tradeoff between keeping the dilationsmall and simulating alarge hypercube. Our main result shows that at the cost ofO (1) dilation asn→ ∞, one can embed a hypercube of near optimum dimension into the star or pancake networksS(n) orP(n). More precisely, lettingQ (d) be the hypercube of dimensiond, our main theorem is stated below. For simplicity, we state it only in the special case when the star network dimension is a power of 2. A more general result (applying to star networks of arbitrary dimension) is obtained by a simple interpolation. This author's research was done during the Spring Semester 1991, as a visiting professor in the Department of Mathematics and Statistics at Miami University.     

Efficiently searching a graph by a smell-oriented vertex process

Efficient graph search is a central issue in many aspects of AI. In most of existing work there is a distinction between the active “searcher”, which both executes the algorithm and holds the memory, and the passive “searched graph”, over which the searcher has no control at all. Large dynamic networks like the Internet, where the nodes are powerful computers and the links have narrow bandwidth and are heavily-loaded, call for a different paradigm, in which most of the burden of computing and memorizing is moved from the searching agent to the nodes of the network. In this paper we suggest a method for searching an undirected, connected graph using the Vertex-Ant-Walk method, where an a(ge)nt walks along the edges of a graph G, occasionally leaving “pheromone” traces at nodes, and using those traces to guide its exploration. We show that the ant can cover the graph within time O(nd), where n is the number of vertices and d the diameter of G. The use of traces achieves a trade-off between random and self-avoiding walks, as it dictates a lower priority for already-visited neighbors. Further properties of the suggested method are: (a) modularity: a group of searching agents, each applying the same protocol, can cooperate on a mission of covering a graph with minimal explicit communication between them; (b) possible convergence to a limit cycle: a Hamiltonian path in G (if one exists) is a possible limit cycle of the process. This revised version was published online in June 2006 with corrections to the Cover Date.     

Prevention of Black Hole Attack in Multicast Routing Protocols for Mobile Ad-Hoc Networks Using a Self-Organized Public Key Infrastructure

ABSTRACT

A mobile ad-hoc network (MANET) is an autonomous system of mobile nodes connected by wireless links in which nodes cooperate by forwarding packets for each other thereby enabling communication beyond direct wireless transmission range. Example applications include battlefield communication, disaster recovery operations, and mobile conferencing. The dynamic nature of ad-hoc networks makes them more vulnerable to security attacks compared with fixed networks. Providing security in mobile ad-hoc networks has been a major issue in recent years. Most of the secure routing protocols proposed by researchers need a centralized authority or a trusted third party to provide authentication. This destroys the self-organizing nature of ad-hoc networks. Black Hole attack is one of the routing attacks that occur in MANETs. In this attack, a malicious node uses the routing protocol to advertise itself as having the shortest path to the node whose packets it wants to intercept. In this article, we propose an enhanced certificate based authentication mechanism, where nodes authenticate each other by issuing certificates to neighboring nodes and generating public key without the need of any online centralized authority. The proposed scheme uses Multicast Ad-hoc On Demand Distance Vector Routing (MAODV) protocol as a support for certification. The effectiveness of our mechanism is illustrated by simulations conducted using network simulator ns-2.     

On the rate of convergence of 2-term recursions in ℝ d

LetG be a compact set in ℝ ^d d≥1,M=G×G andϕ:M →G a map inC ₃(M). Suppose thatϕ has a fixed pointξ, i.e.ϕ(ξ, ξ)=ξ. We investigate the rate of convergence of the iterationx ⁿ⁺²=φ(x ⁿ⁺¹,x ⁿ) withx ⁰,x ¹∈G andx ⁿ→ξ. Iff _n=Q‖x ⁿ−ξ‖ with a suitable norm and a constantQ depending onξ, an exact representation forf _n is derived. The error terms satisfyf _2m+1≍(ƒ_2m)^γ,f _2m+2≍(ƒ_2m+1)^2γ,m≥0, with 1<gg<2, andγ=γ(x ¹,x ⁰). According to our main result we have lim_n→∞{‖x ⁿ⁺²‖/(‖x ⁿ‖)²}=Q, 0<Q<∞. This paper constitutes an extension of a part of the author’s doctoral thesis realized under the direction of Prof. E. Wirsing and Prof. A. Peyerimhoff, University of Ulm (Germany).     

Necessary conditions for infinite-dimensional control problems

We consider infinite-dimensional nonlinear programming problems which consist of minimizing a functionf ₀(u) under a target set constraint. We obtain necessary conditions for minima that reduce to the Kuhn-Tucker conditions in the finite-dimensional case. Among other applications of these necessary conditions and related results, we derive Pontryagin’s maximum principle for a class of control systems described by semilinear equations in Hilbert space and study convergence properties of sequences of near-optimal controls for these systems. The work of this author was supported in part by the National Science Foundation under Grant DMS-8701877.     

Study of General Icomplete Star Interconnection Networks

The star networks,which were originally proposed by Akers and Harel,have suffered from a rigorous restriction on the number of nodes.The general incomplete star networks(GISN) are proposed in this paper to relieve this restriction.An efficient labeling scheme for GISN is given,and routing and broadcasting algorithms are also presented for GIS.The communication diameter of GISN is shown to be bounded by 4n-7.The proposed single node broadcasting algorithm is optimal with respect to time complexity O(nlog2n).     

Approximation Algorithm for Bottleneck Steiner Tree Problem in the Euclidean Plane

A special case of thebottleneck Steiner tree problem in the Euclidean plane was considered in this paper. The problem has applications in the design of wireless communication networks, multifacility location, VLSI routing and network routing. For the special case which requires that there should be no edge connecting any two Steiner points in the optimal solution, a 3-restricted Steiner tree can be found indicating the existence of the performance ratio √2. In this paper, the special case of the problem is proved to beNP-hard and cannot be approximated within ratio √2. First a simple polynomial time approximation algorithm with performance ratio √2 is presented. Then based on this algorithm and the existence of the 3-restricted Steiner tree, a polynomial time approximation algorithm with performance ratio—√2+∈ is proposed, for any ∈>0. Supported partially by Shandong Province Excellent Middle-Aged and Young Scientists Encouragement Fund (Grant No.03BS004) and the Ministry of Education Study Abroad Returnees Research Start-up Fund, and the National Natural Science Foundation of China (Grant No.60273032).     

W^1,2（Ω）- and X^1,2（Ω）-stability of reaction- diffusion cellular neural networks with delay

With Poincare＇s inequality and auxiliary function applied in a class of retarded cellular neural networks with reaction-diffusion, the conditions of the systems＇ W^1,2（Ω）-exponential and X^1,2（Ω）-asmptotic stability are obtained. The stability conditions containing diffusion term are different from those obtained in the previous papers in their exponential stability conditions. One example is given to illustrate the feasibility of this method in the end.     

DRAGON-Lab—Next generation internet technology experiment platform

Testbed technology is very important in the development of the Internet. Similar to the present internet, next generation internet also starts from testbed. There are two kinds of testbeds, testbed networks like CNGI-CERNET2, Internet2, Geant; testbed systems like PlanetLab, NS2. DRAGON-Lab can be viewed as both testbed network and testbed system. DRAGON-Lab is an independent AS （autonomous system） and connected to multiple real networks. On the other hand, DRAGON-Lab integrates many resources of its own, partners＇ and internet＇s, so as to provide open service. DRAGON-Lab has a large scale, provides open service, supports remote visualized experiments and programmable experiments. More details will be introduced in this paper.     

Nonlocal quasi-Newton method for solving convex variational inequalities

Conclusion In the optimization problem [f ₀(x)│h_i(x)<-0,i=1,…,l] relaxation of the functionf ₀(x)+Nh⁺(x) does not produce, as we know [6, 7], α_k=1 in Newton's method with the auxiliary problem (5), (6), whereF(x)=f _0′(x). For this reason, Newton type methods based on relaxation off ₀(x)+Nh⁺(x) are not superlinearly convergent (so-called Maratos effect). The results of this article indicate that if (F(x)=f _0′(x), then replacement of the initial optimization problem with a larger equivalent problem (7) eliminates the Maratos effect in the proposed quasi-Newton method. This result is mainly of theoretical interest, because Newton type optimization methods in the space of the variablesx ∈R ⁿ are less complex. However to the best of our knowledge, the difficulties with nonlocal convergence arising in these methods (choice of parameters, etc.) have not been fully resolved [10, 11]. The discussion of these difficulties and comparison with the proposed method fall outside the scope of the present article, which focuses on solution of variational inequalities (1), (2) for the general caseF′(x)≠F′ ^T(x). Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 78–91, November–December, 1994.