We study distributed algorithms for three graph-theoretic problems in weighted trees and weighted planar graphs. For trees, we present an efficient deterministic distributed algorithm which finds an almost exact appro...
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We study distributed algorithms for three graph-theoretic problems in weighted trees and weighted planar graphs. For trees, we present an efficient deterministic distributed algorithm which finds an almost exact approximation of a maximum-weight matching. In addition, in the case of trees, we show how to approximately solve the minimum-weight dominating set problem. For planar graphs, we present an almost exact approximation for the maximum-weight independent set problem. (C) 2005 Elsevier *** rights reserved.
Colonies of the arboreal turtle ant create networks of trails that link nests and food sources on the graph formed by branches and vines in the canopy of the tropical forest. Ants put down a volatile pheromone on the ...
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Colonies of the arboreal turtle ant create networks of trails that link nests and food sources on the graph formed by branches and vines in the canopy of the tropical forest. Ants put down a volatile pheromone on the edges as they traverse them. At each vertex, the next edge to traverse is chosen using a decision rule based on the current pheromone level. There is a bidirectional flow of ants around the network. In a previous field study, it was observed that the trail networks approximately minimize the number of vertices, thus solving a variant of the popular shortest path problem without any central control and with minimal computational resources. We propose a biologically plausible model, based on a variant of the reinforced random walk on a graph, which explains this observation and suggests surprising algorithms for the shortest path problem and its variants. Through simulations and analysis, we show that when the rate of flow of ants does not change, the dynamics converges to the path with the minimum number of vertices, as observed in the field. The dynamics converges to the shortest path when the rate of flow increases with time, so the colony can solve the shortest path problem merely by increasing the flow rate. We also show that to guarantee convergence to the shortest path, bidirectional flow and a decision rule dividing the flow in proportion to the pheromone level are necessary, but convergence to approximately short paths is possible with other decision rules.
Operator placement plays a key role in reducing the aggregate network overhead within a wireless sensor network (WSN) to extend battery life and the longevity of the network. Consequently, optimal algorithms for the o...
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Operator placement plays a key role in reducing the aggregate network overhead within a wireless sensor network (WSN) to extend battery life and the longevity of the network. Consequently, optimal algorithms for the operator placement problem (OPP) are of paramount importance to WSN performance. Unfortunately, the OPP becomes NP-complete when capacity constraints on the WSN nodes are taken into account. There are many algorithms in the literature that tackle the OPP;however, most of them consider tree-structured query graphs without limitations regarding the operators hosted by the WSN nodes. Therefore, there is a need to propose sophisticated approaches such that the problem is solved in an effective fashion. In this paper, we propose a fully distributed approach that takes into account the WSN node capacity constraints. The proposed approach is thoroughly evaluated through simulations and the results reveal that the proposed approach is superior to several state-of-the-art algorithms, such as DRA, DBA, MCFA, dFNS, and GRAL* found in the literature.
Rate adaptive media streams bear similarities to both elastic (e.g., file transfer) and inelastic (e.g., voice) network traffic classes. As such a service model for streaming media should incorporate characteristics o...
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Rate adaptive media streams bear similarities to both elastic (e.g., file transfer) and inelastic (e.g., voice) network traffic classes. As such a service model for streaming media should incorporate characteristics of both classes: guaranteed minimum rates (for minimally acceptable quality of service (QoS)) and an efficient mechanism for intelligently allocating excess capacity among the competing streams. In this paper we apply the system decomposition Kelly (Charging and rate control for elastic traffic. European Transactions on Communications 8:33-37, 1997) and distributed algorithms framework Kelly et al. (Rate control in communication networks: shadow prices, proportional fairness, and stability. J Oper Res Soc 49:237-252, 1998), developed by Frank Kelly et al. in the context of elastic traffic, to a service model for rate adaptive media streams. Our aim is to allocate excess capacity among competing streams so as to maximize a weighted client-average QoS, where each client QoS is defined as the time-average utility of the instantaneous received rate. We develop the corresponding system decomposition and distributed algorithms appropriate for rate adaptive media streams. Two distinct classes of distributed algorithms are derived: i) a distributed algorithm for dynamic adaptation, where the instantaneous subscription level of each stream is adjusted in response to network updates on route congestion levels, and ii) a distributed algorithm for static adaptation. The stationary point of the static adaptation algorithm is an admission policy that assigns each stream a fixed (in time) transmission rate as a function of the stream volume (the total number of bits associated with the media object). Our results, consistent with earlier work Weber and de Veciana (Rate adaptive multimedia streams: optimization and admisssion control. IEEE/ACM Trans Netw 13(6):1275-1288, December 2005a), confirm the intuitive idea that client average QoS is maximized by granting preferen
By considering the existence of bridge sensor nodes that lose the capability of sensing, the average bridge consensus problem aims to achieve the average of selective observations only from sensing nodes while bridge ...
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ISBN:
(纸本)9781509021826
By considering the existence of bridge sensor nodes that lose the capability of sensing, the average bridge consensus problem aims to achieve the average of selective observations only from sensing nodes while bridge nodes play the role of relaying information. We note that traditional average consensus algorithms achieve the global average of states from all nodes in the network, which are not directly applied here. In this paper we present two distributed algorithms for solving the bridge consensus problem on fixed-tree networks in finite time and a class of time-varying networks exponentially fast, respectively. Both theoretical and numerical results are provided for validations of the proposed algorithms.
In this paper we study the unsplittable flow problem (UFP) on tree networks in a distributed setting. We have a set of processors (or agents) and a set of tree networks defined over some vertex set. Each processor can...
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ISBN:
(纸本)9780769549712
In this paper we study the unsplittable flow problem (UFP) on tree networks in a distributed setting. We have a set of processors (or agents) and a set of tree networks defined over some vertex set. Each processor can access a subset of the tree networks. Each edge in each of the tree networks is associated with a capacity. Each processor has a demand specified as a pair of vertices.. and.., along with a profit and a height;the processor wishes to send data between.. and.. and requires bandwidth equal to its height. Towards that goal, the processor needs to select a tree network accessible to it. A feasible solution selects a subset of demands and schedules each selected demand on a tree network accessible to the processor owning the demand. The requirement is that for any tree network and any edge in the network, the sum of heights of demands scheduled on the network and passing through the edge must not exceed the capacity offered by the edge. The goal is to output a solution having the maximum aggregate profit. Prior work has addressed the above problem in a distributed setting for the special case where all the edge capacities are uniform, say one unit. The main contributions of this paper is to address the general case where the edge capacities can be non-uniform and arbitrary. For this case, we present distributed algorithms with poly-logarithmic approximation ratio.
We consider the problem of computing local clusters in large graphs distributed across nodes in a network using two different models of distributed computation. We give a distributed algorithm that computes a local cl...
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ISBN:
(纸本)9783319267845;9783319267838
We consider the problem of computing local clusters in large graphs distributed across nodes in a network using two different models of distributed computation. We give a distributed algorithm that computes a local cluster in time that depends only logarithmically on the size of the graph in the CONGEST model. In particular, when the conductance of the optimal local cluster is known, the algorithm runs in time entirely independent of the size of the graph and depends only on error bounds for approximation. We also show that the local cluster problem can be computed in the k-machine distributed model in sublinear time. The speedup of our local cluster algorithms is mainly due to the use of our distributed algorithm for heat kernel pagerank.
Since its inception, the concept of network coordinates has been proposed to solve a wide variety of problems such as overlay optimization, network routing, network localization, and network modeling. However, two pra...
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ISBN:
(纸本)9781605583341
Since its inception, the concept of network coordinates has been proposed to solve a wide variety of problems such as overlay optimization, network routing, network localization, and network modeling. However, two practical problems significantly limit the applications of network coordinates today. First, how can network coordinates be stabilized without losing accuracy so that they can be cached by applications? Second, how can network coordinates be secured Such that legitimate nodes' coordinates are not impacted by misbehaving nodes? Although these problems have been discussed extensively, solving them in decentralized network coordinates systems remains an open problem. This paper presents new distributed algorithms to solve the coordinates stability and security problems. For the stability problem, we propose an error elimination model that can achieve stability without hurting accuracy. A novel algorithm based on this model is presented. For the security problem, we show that recently proposed statistical detection mechanisms cannot achieve an acceptable level of security against even simple attacks. We propose to address the security problem in two parts. First, we show how the computation of coordinates can be protected by a customized Byzantine fault detection algorithm. Second, we adopt a triangle inequality violation detection algorithm to protect delay measurements. These algorithms can be integrated together to provide stable and secure network coordinates.
The opportunistic spectrum access (OSA) algorithms aim to maximize network throughput by ensuring orthogonal channel allocation among secondary users (SUs) in cognitive radio network (CRN). OSA is challenging in the d...
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ISBN:
(纸本)9781538611821
The opportunistic spectrum access (OSA) algorithms aim to maximize network throughput by ensuring orthogonal channel allocation among secondary users (SUs) in cognitive radio network (CRN). OSA is challenging in the decentralized CRN due to lack of coordination among SUs. Most of the existing algorithms assume prior knowledge of the number of active SUs to guarantee orthogonalization. In addition, they assume static network only where all SUs stay in the network throughout the horizon which is not feasible in practical conditions. However the dynamic network may also exist where the SUs can enter or exit the network at any time. Also, most of the existing algorithms assume an i.i.d. reward model whereas a markovian model may be more appropriate where the rewards are assumed to come from a finite, irreducible and aperiodic Markov chain represented by a single parameter probability transition matrix. Thus, our goal is to design a distributed algorithm for decentralized static and dynamic network without prior knowledge of the number of active SUs with i.i.d. as well as markovian reward model.
We briefly recall the paradigm for distributed stochastic approximation with consensus introduced by Tsitsiklis et al and describe some recent 'nonlinear' versions of it. Some possible future directions will a...
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ISBN:
(纸本)9781728101248
We briefly recall the paradigm for distributed stochastic approximation with consensus introduced by Tsitsiklis et al and describe some recent 'nonlinear' versions of it. Some possible future directions will also be indicated.
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