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12
Constanttime distributed scheduling policies for ad hoc wireless networks
 in Proceedings of IEEE Conference on Decision and Control
, 2006
"... Abstract — We propose two new distributed scheduling policies for ad hoc wireless networks that can achieve provable capacity regions. Known scheduling policies that guarantee comparable capacity regions are either centralized or need computation time that increases with the size of the network. In ..."
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Cited by 48 (5 self)
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Abstract — We propose two new distributed scheduling policies for ad hoc wireless networks that can achieve provable capacity regions. Known scheduling policies that guarantee comparable capacity regions are either centralized or need computation time that increases with the size of the network. In contrast, the unique feature of the proposed distributed scheduling policies is that they are constanttime policies, i.e., the time needed for computing a schedule is independent of the network size. Hence, they can be easily deployed in large networks. I.
A parallel approximation algorithm for the weighted maximum matching problem
 In Proc. Seventh Int. Conf. on Parallel Processing and Applied Mathematics (PPAM
, 2007
"... Abstract. We consider the problem of computing a weighted edge matching in a large graph using a parallel algorithm. This problem has application in several areas of combinatorial scientific computing. Since an exact algorithm for the weighted matching problem is both fairly expensive to compute and ..."
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Cited by 8 (2 self)
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Abstract. We consider the problem of computing a weighted edge matching in a large graph using a parallel algorithm. This problem has application in several areas of combinatorial scientific computing. Since an exact algorithm for the weighted matching problem is both fairly expensive to compute and hard to parallelise we instead consider fast approximation algorithms. We analyse a distributed algorithm due to Hoepman [8] and show how this can be turned into a parallel algorithm. Through experiments using both complete as well as sparse graphs we show that our new parallel algorithm scales well using up to 32 processors. 1
WEIGHTED MATCHING IN THE SEMISTREAMING MODEL
, 2008
"... We reduce the best known approximation ratio for finding a weighted matching of a graph using a onepass semistreaming algorithm from 5.828 to 5.585. The semistreaming model forbids random access to the input and restricts the memory to O(n · polylog n) bits. It was introduced by Muthukrishnan in ..."
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Cited by 8 (0 self)
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We reduce the best known approximation ratio for finding a weighted matching of a graph using a onepass semistreaming algorithm from 5.828 to 5.585. The semistreaming model forbids random access to the input and restricts the memory to O(n · polylog n) bits. It was introduced by Muthukrishnan in 2003 and is appropriate when dealing with massive graphs.
Linear Programming in the Semistreaming Model with Application to the Maximum Matching Problem
, 2012
"... In this paper we study linearprogramming based approaches to the maximum matching problem in the semistreaming model. In this model edges are presented sequentially, possibly in an adversarial order, and we are only allowed to use a small space. The allowed space is near linear in the number of ve ..."
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Cited by 5 (1 self)
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In this paper we study linearprogramming based approaches to the maximum matching problem in the semistreaming model. In this model edges are presented sequentially, possibly in an adversarial order, and we are only allowed to use a small space. The allowed space is near linear in the number of vertices (and sublinear in the number of edges) of the input graph. The semistreaming model is relevant in the context of processing of very large graphs. In recent years, there have been several new and exciting results in the semistreaming model. However broad techniques such as linear programming have not been adapted to this model. In this paper we present several techniques to adapt and optimize linearprogramming based approaches in the semistreaming model. We use the maximum matching problem as a foil to demonstrate the e ectiveness of adapting such tools in this model. As a consequence we improve almost all previous results on the semistreaming maximum matching problem. We also prove new results on interesting variants.
PrivacyPreserving Event Detection in Pervasive Spaces
"... Pervasive applications often require gathering information about individuals that may be considered sensitive. Often, one is forced to make a difficult choice: either to risk loss of privacy or to forgo the benefits that pervasive technology offers. Our conjecture is that it is possible to design an ..."
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Cited by 5 (3 self)
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Pervasive applications often require gathering information about individuals that may be considered sensitive. Often, one is forced to make a difficult choice: either to risk loss of privacy or to forgo the benefits that pervasive technology offers. Our conjecture is that it is possible to design and deploy applications in a pervasive environment that do not come at the expense of individuals ’ privacy. In this paper, we consider eventdriven pervasive spaces where multimedia streams captured by sensors embedded in the infrastructure are used to detect a variety of applicationspecific media events. In particular we develop a systems architecture for deploying a surveillance application in such an environment. The privacy challenge corresponds to that of detecting only events that break certain rules without disclosing any identifying information unless necessary. We characterize the nature of various inference channels that arise in designing such a system and determine appropriate security constraints that need to be met. We model privacypreserving event detection as an optimization problem that attempts to balance disclosure and performance in such a system, and design efficient communication protocols for our proposed architecture. 1
Scaling algorithms for approximate and exact maximum weight matching
, 2011
"... The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the ..."
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Cited by 3 (0 self)
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The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the following sense. For any ɛ> 0, we give an algorithm that computes a (1 − ɛ)approximate maximum weight matching in O(mɛ −1 log ɛ −1) time, that is, optimal linear time for any fixed ɛ. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error. Our second contribution is a new exact maximum weight matching algorithm for integerweighted bipartite graphs that runs in time O(m √ n log N). This improves on the O(Nm √ n)time and O(m √ n log(nN))time algorithms known since the mid 1980s, for 1 ≪ log N ≪ log n. Here N is the maximum integer edge weight. 1
Minimum Time Point Assignment for Coverage by Two Constrained Robots
"... Abstract — This paper focuses on the assignment of discrete points to two robots, in the presence of geometric and kinematic constraints between the robots. The individual points have differing processing times, and the goal is to identify an assignment of points to the robots so that the total proc ..."
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Cited by 2 (2 self)
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Abstract — This paper focuses on the assignment of discrete points to two robots, in the presence of geometric and kinematic constraints between the robots. The individual points have differing processing times, and the goal is to identify an assignment of points to the robots so that the total processing time is minimized. The assignment of points to the robots is the first step in the path generation process for the robots. This work is motivated by an industrial microelectronics manufacturing system with two robots, with square footprints, that are constrained to translate along a common line while satisfying proximity and collision avoidance constraints. The N points lie on a planar base plate that can translate along the plane normal to the direction of motion of the robots. The geometric constraints on the motions of the two robots lead to constraints on points that can be processed simultaneously. We show that the point assignment for processing problem can be converted to a maximum weighted matching problem on a graph and solved optimally in O(N 3) time. Since this is too slow for large datasets, we present a O(N 2) time greedy algorithm and prove that the greedy solution is within a factor of 3/2 of the optimal solution. Finally, we provide computational results for the greedy algorithm on typical industrial datasets. I.
Coverage of a Planar Point Set with Multiple Constrained Robots
, 2007
"... An important problem that arises in many applications is: Given k robots with known processing footprint to process a set of N points in the plane, find trajectories for each robot satisfying the geometric, kinematic, and dynamic constraints such that the time required to cover the points (processi ..."
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Cited by 2 (2 self)
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An important problem that arises in many applications is: Given k robots with known processing footprint to process a set of N points in the plane, find trajectories for each robot satisfying the geometric, kinematic, and dynamic constraints such that the time required to cover the points (processing time plus travel time) is minimized. This problem is a hybrid discretecontinuous optimization problem and is hard to solve optimally even for k = 1. One approach is to treat this as a two stage problem where the first stage is to find the best possible path satisfying the geometric constraints and then convert it into a trajectory satisfying the differential constraints. In this paper, we consider an industrial microelectronics manufacturing system of k( = 2) robots, with square footprints, that are constrained to translate along a line while satisfying proximity constraints. The points lie on a planar base plate that can translate along the plane normal to the direction of motion of the robots. We solve the geometric problem of path generation for the robots using a two step approach that yields a suboptimal solution: 1) Minimize the number of k−tuples subject to geometric constraints. 2) Solve a Traveling Salesman Problem (TSP) in the k−tuple space with an appropriately defined metric to minimize the total travel cost. We show that for k = 2, step 1 can be converted to a maximum cardinality matching problem on a graph and solved optimally in polynomial time. The matching algorithm takes O(N 3) time in general and is too slow for large datasets. Therefore, we also provide a greedy algorithm for step 1 that takes O(N log N) time. We provide computational results comparing the two approaches and show that the greedy algorithm is very close to the optimal solution for large datasets. We also provide local search based heuristics to improve the TSP tour in the pair space and give preliminary implementation results showing an improvement of 1 % to 2 % in the resultant tour.
A Selfstabilizing Weighted Matching Algorithm
"... Abstract. The problem of computing a matching in a graph involves creating pairs of neighboring nodes such that no node is paired more than once. Previous work on the matching problem has resulted in several selfstabilizing algorithms for finding a maximal matching in an unweighted graph. In this pa ..."
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Cited by 1 (0 self)
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Abstract. The problem of computing a matching in a graph involves creating pairs of neighboring nodes such that no node is paired more than once. Previous work on the matching problem has resulted in several selfstabilizing algorithms for finding a maximal matching in an unweighted graph. In this paper we present the first selfstabilizing algorithm for the weighted matching problem. We show that the algorithm computesapproximation to the optimal solution. The algorithm is simple and uses only a fixed number of variables per node. Stabilization is shown under various types of daemons. a 1 2
1 PrivacyPreserving Event Detection in Pervasive Spaces
"... Abstract — In this paper, we consider privacy challenges in eventdriven pervasive spaces where multimedia streams captured by sensors embedded in the infrastructure are used to detect a variety of applicationspecific media events. In particular, we develop techniques to detect events without discl ..."
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Abstract — In this paper, we consider privacy challenges in eventdriven pervasive spaces where multimedia streams captured by sensors embedded in the infrastructure are used to detect a variety of applicationspecific media events. In particular, we develop techniques to detect events without disclosing any identifying information unless necessary. We characterize the nature of inference channels that arise and model privacy preserving event detection as an optimization problem that attempts to balance disclosure with performance. We design and test efficient communication protocols that realize this tradeoff. I.