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48
Message ferrying: Proactive routing in highlypartitioned wireless ad hoc networks
, 2003
"... An ad hoc network allows devices with wireless interfaces to communicate with each other without any preinstalled infrastructure. Due to node mobility, limited radio power, node failure and wide deployment area, ad hoc networks are often vulnerable to network partitioning. A number of examples are i ..."
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Cited by 87 (5 self)
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An ad hoc network allows devices with wireless interfaces to communicate with each other without any preinstalled infrastructure. Due to node mobility, limited radio power, node failure and wide deployment area, ad hoc networks are often vulnerable to network partitioning. A number of examples are in battlefield, disaster recovery and wide area surveillance. Unfortunately, most existing ad hoc routing protocols will fail to deliver messages under these circumstances since no route to the destination exists. In this work, we propose the Message Ferrying or MF scheme that provides efficient data delivery in disconnected ad hoc networks. In the MF scheme, nodes move proactively to send or receive messages. By introducing nonrandomness in a node’s proactive movement and exploiting such nonrandomness to deliver messages, the MF scheme improves data delivery performance in a disconnected network. In this paper, we propose the basic design of the MF scheme and develop a general framework to classify variations of MF systems. We also study ferry route design problem in stationary node case which is shown to be NPhard and provide an efficient algorithm to compute ferry route. 1
A constantfactor approximation algorithm for the kMST problem
 In Proc. of ACM symposium on Theory of computing (STOC ’96
, 1996
"... In the Euclidean TSP with neighborhoods (TSPN) problem we seek a shortest tour that visits a given set of n neighborhoods. The Euclidean TSPN generalizes the standard TSP on points. We present the first constantfactor approximation algorithm for TSPN on an arbitrary set of disjoint, connected neigh ..."
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Cited by 49 (5 self)
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In the Euclidean TSP with neighborhoods (TSPN) problem we seek a shortest tour that visits a given set of n neighborhoods. The Euclidean TSPN generalizes the standard TSP on points. We present the first constantfactor approximation algorithm for TSPN on an arbitrary set of disjoint, connected neighborhoods in the plane. Prior approximation bounds were O(log n), except in special cases. Our approximation algorithm applies to arbitrary connected neighborhoods of any size or shape. 1
Stochastic event capture using mobile sensors subject to a quality metric
 in Proc. of ACM MobiCom
, 2006
"... Mobile sensors cover more area over a period of time than the same number of stationary sensors. However, the quality of coverage achieved by mobile sensors depends on the velocity, mobility pattern, number of mobile sensors deployed and the dynamics of the phenomenon being sensed. The gains attaine ..."
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Cited by 40 (0 self)
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Mobile sensors cover more area over a period of time than the same number of stationary sensors. However, the quality of coverage achieved by mobile sensors depends on the velocity, mobility pattern, number of mobile sensors deployed and the dynamics of the phenomenon being sensed. The gains attained by mobile sensors over static sensors and the optimal motion strategies for mobile sensors are not well understood. In this paper we consider the problem of event capture using mobile sensors. The events of interest arrive at certain points in the sensor field and fade away according to arrival and departure time distributions. An event is said to be captured if it is sensed by one of the mobile sensors before it fades away. For this scenario we analyze how the quality of coverage scales with the velocity, path and number of mobile sensors. We characterize the cases where the deployment of mobile sensors has
On the complexity of approximating TSP with neighborhoods and related problems
 Computational Complexity
"... We prove that various geometric covering problems, related to the Travelling Salesman Problem cannot be efficiently approximated to within any constant factor unless P = NP. This includes the GroupTravelling Salesman Problem (TSP with Neighborhoods) in the Euclidean plane, the GroupSteinerTree in ..."
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Cited by 30 (2 self)
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We prove that various geometric covering problems, related to the Travelling Salesman Problem cannot be efficiently approximated to within any constant factor unless P = NP. This includes the GroupTravelling Salesman Problem (TSP with Neighborhoods) in the Euclidean plane, the GroupSteinerTree in the Euclidean plane and the Minimum Watchman Tour and the Minimum Watchman Path in 3D. It resolves three open problems presented in the comprehensive survey of Mitchell [Mit00], improves a previously known approximation hardness factor of 2041 2040 [GL00, dBGK+ 02] for the first problem, and it is the first approximation hardness factor for the other problems. Some inapproximability factors are also shown for special cases of the above problems, where the size of the sets is bounded. GroupTSP and GroupSteinerTree where each neighbourhood is connected are also considered. It is shown that approximating these variants to within any constant factor smaller than 2, is NPhard. For the GroupTravelling Salesman and GroupSteinerTree Problems in dimension d, we show an innapproximability factor of O(log d−1 d HyperGraph VertexCover.
On trip planning queries in spatial databases
 In SSTD
, 2005
"... In this paper we discuss a new type of query in Spatial Databases, called the Trip Planning Query (TPQ). Given a set of points of interest P in space, where each point belongs to a specific category, a starting point S and a destination E, TPQ retrieves the best trip that starts at S, passes through ..."
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Cited by 28 (1 self)
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In this paper we discuss a new type of query in Spatial Databases, called the Trip Planning Query (TPQ). Given a set of points of interest P in space, where each point belongs to a specific category, a starting point S and a destination E, TPQ retrieves the best trip that starts at S, passes through at least one point from each category, and ends at E. For example, a driver traveling from Boston to Providence might want to stop to a gas station, a bank and a post office on his way, and the goal is to provide him with the best possible route (in terms of distance, traffic, road conditions, etc.). The difficulty of this query lies in the existence of multiple choices per category. In this paper, we study fast approximation algorithms for TPQ in a metric space. We provide a number of approximation algorithms with approximation ratios that depend on either the number of categories, the maximum number of points
Approximation algorithms for Euclidean group TSP
 In Automata, languages and programming : 32nd International Colloquim, ICALP 2005
, 2005
"... Abstract. In the Euclidean group Traveling Salesman Problem (TSP), we are given a set of points P in the plane and a set of m connected regions, each containing at least one point of P. We want to find a tour of minimum length that visits at least one point in each region. This unifies the TSP with ..."
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Cited by 18 (4 self)
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Abstract. In the Euclidean group Traveling Salesman Problem (TSP), we are given a set of points P in the plane and a set of m connected regions, each containing at least one point of P. We want to find a tour of minimum length that visits at least one point in each region. This unifies the TSP with Neighborhoods and the Group Steiner Tree problem. We give a (9.1α + 1)approximation algorithm for the case when the regions are disjoint αfat objects with possibly varying size. This considerably improves the best results known, in this case, for both the group Steiner tree problem and the TSP with Neighborhoods problem. We also give the first O(1)approximation algorithm for the problem with intersecting regions. 1
Minimumcost coverage of point sets by disks
 in Symposium on Computational Geometry
, 2006
"... We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (t j) and radii (r j) that cover a given set of demand points Y ⊂ R 2 at the smallest possible cost. We consider cost functions of the form ∑ j f(r j), where f(r) = ..."
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Cited by 16 (3 self)
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We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (t j) and radii (r j) that cover a given set of demand points Y ⊂ R 2 at the smallest possible cost. We consider cost functions of the form ∑ j f(r j), where f(r) = r α is the cost of transmission to radius r. Special cases arise for α = 1 (sum of radii) and α = 2 (total area); power consumption models in wireless network design often use an exponent α> 2. Different scenarios arise according to possible restrictions on the transmission centers t j, which may be constrained to belong to a given discrete set or to lie on a line, etc. We obtain several new results, including (a) exact and approximation algorithms for selecting transmission points t j on a given line in order to cover demand points Y ⊂ R 2; (b) approximation algorithms (and an algebraic intractability result) for selecting an optimal line on which to place transmission points to cover Y; (c) a proof of NPhardness for a discrete set of transmission points in R 2 and any fixed α> 1; and (d) a polynomialtime approximation scheme for the problem of computing a minimum cost covering tour (MCCT), in which the total cost is a linear combination of the transmission cost for the set of disks and the length of a tour/path that connects the centers of the disks. ACM Classification: F.2.2 Nonnumerical Algorithms and Problems. AMS Classification: 68Q25, 68U05, 90C27.
TSP with neighborhoods of varying size
 J. ALGORITHMS
, 2005
"... In TSP with neighborhoods (TSPN) we are given a collection S of regions in the plane, called neighborhoods, and we seek the shortest tour that visits all neighborhoods. Until now constantfactor approximation algorithms have been known only for cases where the neighborhoods are of approximately the ..."
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Cited by 6 (0 self)
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In TSP with neighborhoods (TSPN) we are given a collection S of regions in the plane, called neighborhoods, and we seek the shortest tour that visits all neighborhoods. Until now constantfactor approximation algorithms have been known only for cases where the neighborhoods are of approximately the same size. In this paper we present the first polynomial time constantfactor approximation algorithm for disjoint convex fat neighborhoods of arbitrary size. We also show that in the general case, where the neighborhoods can overlap and are not required to be convex or fat, TSPN is APXhard and cannot be approximated within a factor of 391/390 in polynomialtime, unless P=NP.
Approximation Schemes for the Generalized Geometric Problems with Geographic Clustering
 EWCG 2005
, 2005
"... This paper is concerned with polynomial time approximations schemes for the generalized geometric problems with geographic clustering. We illustrate the approach on the generalized traveling salesman problem which is also known as GroupTSP or TSP with neighborhoods. We prove that under the conditio ..."
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Cited by 5 (1 self)
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This paper is concerned with polynomial time approximations schemes for the generalized geometric problems with geographic clustering. We illustrate the approach on the generalized traveling salesman problem which is also known as GroupTSP or TSP with neighborhoods. We prove that under the condition that all regions are nonintersecting and have comparable sizes and shapes, the problem admits PTAS. To derive a PTAS we extend the algorithm by Arora [2]. This extension involves the dissection mechanism and solution of the selection problem. We observe that the results are applicable to many generalized geometric problems, to other Minkowski norms, and to other fixed dimensional spaces.
Minimumperimeter intersecting polygons, Algorithmica
 Journal of Algorithms
"... Given a set S of segments in the plane, a polygon P is an intersecting polygon of S if every segment in S intersects the interior or the boundary of P. The problem MPIP of computing a minimumperimeter intersecting polygon of a given set of n segments in the plane was first considered by Rappaport i ..."
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Cited by 4 (3 self)
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Given a set S of segments in the plane, a polygon P is an intersecting polygon of S if every segment in S intersects the interior or the boundary of P. The problem MPIP of computing a minimumperimeter intersecting polygon of a given set of n segments in the plane was first considered by Rappaport in 1995. This problem is not known to be polynomial, nor it is known to be NPhard. Rappaport (1995) gave an exponentialtime exact algorithm for MPIP. Hassanzadeh and Rappaport (2009) gave a polynomialtime approximation algorithm with ratio π 2 ≈ 1.57. In this paper, we present two improved approximation algorithms for MPIP: a 1.28approximation algorithm by linear programming, and a polynomialtime approximation scheme by discretization and enumeration. Our algorithms can be generalized for computing an approximate minimumperimeter intersecting polygon of a set of convex polygons in the plane. From the other direction, we show that computing a minimumperimeter intersecting polygon of a set of (not necessarily convex) simple polygons is NPhard.