Results 1  10
of
103
Sharing the Cost of Multicast Transmissions
, 2001
"... We investigate costsharing algorithms for multicast transmission. Economic considerations point to two distinct mechanisms, marginal cost and Shapley value, as the two solutions most appropriate in this context. We prove that the former has a natural algorithm that uses only two messages per link o ..."
Abstract

Cited by 284 (16 self)
 Add to MetaCart
(Show Context)
We investigate costsharing algorithms for multicast transmission. Economic considerations point to two distinct mechanisms, marginal cost and Shapley value, as the two solutions most appropriate in this context. We prove that the former has a natural algorithm that uses only two messages per link of the multicast tree, while we give evidence that the latter requires a quadratic total number of messages. We also show that the welfare value achieved by an optimal multicast tree is NPhard to approximate within any constant factor, even for boundeddegree networks. The lowerbound proof for the Shapley value uses a novel algebraic technique for bounding from below the number of messages exchanged in a distributed computation; this technique may prove useful in other contexts as well.
Nearoptimal sensor placements: Maximizing information while minimizing communication cost
 In IPSN
, 2006
"... When monitoring spatial phenomena with wireless sensor networks, selecting the best sensor placements is a fundamental task. Not only should the sensors be informative, but they should also be able to communicate efficiently. In this paper, we present a datadriven approach that addresses the three ..."
Abstract

Cited by 152 (19 self)
 Add to MetaCart
(Show Context)
When monitoring spatial phenomena with wireless sensor networks, selecting the best sensor placements is a fundamental task. Not only should the sensors be informative, but they should also be able to communicate efficiently. In this paper, we present a datadriven approach that addresses the three central aspects of this problem: measuring the predictive quality of a set of sensor locations (regardless of whether sensors were ever placed at these locations), predicting the communication cost involved with these placements, and designing an algorithm with provable quality guarantees that optimizes the NPhard tradeoff. Specifically, we use data from a pilot deployment to build nonparametric probabilistic models called Gaussian Processes (GPs) both for the spatial phenomena of interest and for the spatial variability of link qualities, which allows us to estimate predictive power and communication cost of unsensed locations. Surprisingly, uncertainty in the representation of link qualities plays an important role in estimating communication costs. Using these models, we present a novel, polynomialtime, datadriven algorithm, pSPIEL, which selects Sensor Placements at Informative and costEffective Locations. Our approach exploits two important properties of this problem: submodularity, formalizing the intuition that adding a node to a small deployment can help more than adding a node to a large deployment; and locality, under which nodes that are far from each other provide almost independent information. Exploiting these properties, we prove strong approximation guarantees for our pSPIEL approach. We also provide extensive experimental validation of this practical approach on several realworld placement problems, and built a complete system implementation on 46 Tmote Sky motes, demonstrating significant advantages over existing methods.
The primaldual method for approximation algorithms and its application to network design problems.
, 1997
"... Abstract In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to N P hard problems in combinatorial optimization. Because of parallels with the primaldual method commonly used in combinatorial optimization, we call it the prim ..."
Abstract

Cited by 137 (5 self)
 Add to MetaCart
(Show Context)
Abstract In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to N P hard problems in combinatorial optimization. Because of parallels with the primaldual method commonly used in combinatorial optimization, we call it the primaldual method for approximation algorithms. We show how this technique can be used to derive approximation algorithms for a number of different problems, including network design problems, feedback vertex set problems, and facility location problems.
Approximation Algorithms for Orienteering and DiscountedReward TSP
, 2003
"... In this paper, we give the first constantfactor approximation algorithm for the rooted Orienteering problem, as well as a new problem that we call the DiscountedReward TSP, motivated by robot navigation. In both problems, we are given a graph with lengths on edges and prizes (rewards) on nodes, ..."
Abstract

Cited by 84 (1 self)
 Add to MetaCart
(Show Context)
In this paper, we give the first constantfactor approximation algorithm for the rooted Orienteering problem, as well as a new problem that we call the DiscountedReward TSP, motivated by robot navigation. In both problems, we are given a graph with lengths on edges and prizes (rewards) on nodes, and a start node s. In the Orienteering Problem, the goal is to find a path that maximizes the reward collected, subject to a hard limit on the total length of the path. In the DiscountedReward TSP, instead of a length limit we are given a discount factor fl, and the goal is to maximize total discounted reward collected, where reward for a node reached at time t is discounted by fl . This is similar to the objective considered in Markov Decision Processes (MDPs) except we only receive a reward the first time a node is visited. We also consider tree and multiplepath variants of these problems and provide approximations for those as well. Although the unrooted orienteering problem, where there is no fixed start node s, has been known to be approximable using algorithms for related problems such as kTSP (in which the amount of reward to be collected is fixed and the total length is approximately minimized), ours is the first to approximate the rooted question, solving an open problem of [3, 1].
Pricing WiFi at Starbucks  Issues in Online Mechanism Design
 In Fourth ACM Conf. on Electronic Commerce (EC’03
, 2003
"... We consider the problem of designing mechanisms for online problems in which agents arrive over time and the mechanism is unaware of the agent until the agent announces her arrival. Problems of this sort are becoming extremely common particularly in a wide variety of problems involving wireless n ..."
Abstract

Cited by 57 (13 self)
 Add to MetaCart
(Show Context)
We consider the problem of designing mechanisms for online problems in which agents arrive over time and the mechanism is unaware of the agent until the agent announces her arrival. Problems of this sort are becoming extremely common particularly in a wide variety of problems involving wireless networking.
Efficient Informative Sensing using Multiple Robots
"... The need for efficient monitoring of spatiotemporal dynamics in large environmental applications, such as the water quality monitoring in rivers and lakes, motivates the use of robotic sensors in order to achieve sufficient spatial coverage. Typically, these robots have bounded resources, such as l ..."
Abstract

Cited by 56 (5 self)
 Add to MetaCart
(Show Context)
The need for efficient monitoring of spatiotemporal dynamics in large environmental applications, such as the water quality monitoring in rivers and lakes, motivates the use of robotic sensors in order to achieve sufficient spatial coverage. Typically, these robots have bounded resources, such as limited battery or limited amounts of time to obtain measurements. Thus, careful coordination of their paths is required in order to maximize the amount of information collected, while respecting the resource constraints. In this paper, we present an efficient approach for nearoptimally solving the NPhard optimization problem of planning such informative paths. In particular, we first develop eSIP (efficient Singlerobot Informative Path planning), an approximation algorithm for optimizing the path of a single robot. Hereby, we use a Gaussian Process to model the underlying phenomenon, and use the mutual information between the visited locations and remainder of the space to quantify the amount of information collected. We prove that the mutual information collected using paths obtained by using eSIP is close to the information obtained by an optimal solution. We then provide a general technique, sequential allocation, which can be used to extend any single robot planning algorithm, such as eSIP, for the multirobot problem. This procedure approximately generalizes any guarantees for the singlerobot problem to the multirobot case. We extensively evaluate the effectiveness of our approach on several experiments performed infield for two important environmental sensing applications, lake and river monitoring, and simulation experiments performed using several real world sensor network data sets. 1.
Local search with perturbations for the prizecollecting Steiner tree problem in graphs
 Networks
, 2001
"... Abstract. Given an undirected graph with prizes associated with its nodes and weights associated with its edges, the prizecollecting Steiner tree problem consists of finding a subtree of this graph which minimizes the sum of the weights of its edges plus the prizes of the nodes not spanned. In this ..."
Abstract

Cited by 51 (25 self)
 Add to MetaCart
Abstract. Given an undirected graph with prizes associated with its nodes and weights associated with its edges, the prizecollecting Steiner tree problem consists of finding a subtree of this graph which minimizes the sum of the weights of its edges plus the prizes of the nodes not spanned. In this paper, we describe a multistart local search algorithm for the prizecollecting Steiner tree problem, based on the generation of initial solutions by a primaldual algorithm using perturbed node prizes. Pathrelinking is used to improve the solutions found by local search and variable neighborhood search is used as a postoptimization procedure. Computational experiments involving different algorithm variants are reported. Our results show that the local search with perturbations approach found optimal solutions on nearly all of the instances tested.
Robust submodular observation selection
, 2008
"... In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations wh ..."
Abstract

Cited by 46 (4 self)
 Add to MetaCart
In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations which are robust against a number of possible objective functions. Examples include minimizing the maximum posterior variance in Gaussian Process regression, robust experimental design, and sensor placement for outbreak detection. In this paper, we present the Submodular Saturation algorithm, a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity, an intuitive diminishing returns property. Moreover, we prove that better approximation algorithms do not exist unless NPcomplete problems admit efficient algorithms. We show how our algorithm can be extended to handle complex cost functions (incorporating nonunit observation cost or communication and path costs). We also show how the algorithm can be used to nearoptimally trade off expectedcase (e.g., the Mean Square Prediction Error in Gaussian Process regression) and worstcase (e.g., maximum predictive variance) performance. We show that many important machine learning problems fit our robust submodular observation selection formalism, and provide extensive empirical evaluation on several realworld problems. For Gaussian Process regression, our algorithm compares favorably with stateoftheart heuristics described in the geostatistics literature, while being simpler, faster and providing theoretical guarantees. For robust experimental design, our algorithm performs favorably compared to SDPbased algorithms.
An algorithmic framework for the exact solution of the prizecollecting Steiner tree problem
 MATHEMATICAL PROGAMMING, SERIES B
, 2006
"... The PrizeCollecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of utility ne ..."
Abstract

Cited by 43 (14 self)
 Add to MetaCart
The PrizeCollecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of utility networks where profit generating customers and the network connecting them have to be chosen in the most profitable way. Our main contribution is the formulation and implementation of a branchandcut algorithm based on a directed graph model where we combine several stateoftheart methods previously used for the Steiner tree problem. Our method outperforms the previously published results on the standard benchmark set of problems. We can solve all benchmark instances from the literature to optimality, including some of them for which the optimum was not known. Compared to a recent algorithm by Lucena and Resende, our new method is faster by more than two orders of magnitude. We also introduce a new class of more challenging instances and present computational results for them. Finally, for a set of largescale realworld instances arising in the design of fiber optic networks, we also obtain optimal solution values.
Improved Approximation Algorithms for PRIZECOLLECTING STEINER TREE and TSP
"... We study the prizecollecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a. PATHTSP) problems (PCST, PCTSP, and PCS, respectively): given a graph (V, E) with costs on each edge and a penalty (a.k.a. prize) on each node, the goal is to find a tree (for PCST), cycle (for PCTSP ..."
Abstract

Cited by 30 (6 self)
 Add to MetaCart
(Show Context)
We study the prizecollecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a. PATHTSP) problems (PCST, PCTSP, and PCS, respectively): given a graph (V, E) with costs on each edge and a penalty (a.k.a. prize) on each node, the goal is to find a tree (for PCST), cycle (for PCTSP), or stroll (for PCS) that minimizes the sum of the edge costs in the tree/cycle/stroll and the penalties of the nodes not spanned by it. In addition to being a useful theoretical tool for helping to solve other optimization problems, PCST has been applied fruitfully by AT&T to the optimization of realworld telecommunications networks. The most recent improvements for the first two problems, giving a 2approximation algorithm for each, appeared first in 1992. (A 2approximation for PCS appeared in 2003.) The natural linear programming (LP) relaxation of PCST has an integrality gap of 2, which has been a barrier to further improvements for this problem. We present (2 − ɛ)approximation algorithms for all three problems, connected by a unified technique for improving prizecollecting algorithms that allows us to circumvent the integrality gap barrier.