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57
Approximation algorithms for stochastic orienteering
 SODA
"... In the Stochastic Orienteering problem, we are given a metric, where each node also has a job located there with some deterministic reward and a random size. (Think of the jobs as being chores one needs to run, and the sizes as the amount of time it takes to do the chore.) The goal is to adaptively ..."
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In the Stochastic Orienteering problem, we are given a metric, where each node also has a job located there with some deterministic reward and a random size. (Think of the jobs as being chores one needs to run, and the sizes as the amount of time it takes to do the chore.) The goal is to adaptively decide which nodes to visit to maximize total expected reward, subject to the constraint that the total distance traveled plus the total size of jobs processed is at most a given budget of B. (I.e., we get reward for all those chores we finish by the end of the day). The (random) size of a job is not known until it is completely processed. Hence the problem combines aspects of both the stochastic knapsack problem with uncertain item sizes and the deterministic orienteering problem of using a limited travel time to maximize gathered rewards located at nodes. In this paper, we present a constantfactor approximation algorithm for the best nonadaptive policy for the Stochastic Orienteering problem. We also show a small adaptivity gap—i.e., the existence of a nonadaptive policy whose reward is at least an Ω(1/loglogB) fraction of the optimal expected reward—and hence we also get an O(loglogB)approximation algorithm for the adaptive problem. Finally we address the case when the node rewards are also random and could be correlated with the waiting time, and give a nonadaptive policy which is an O(lognlogB)approximation to the best adaptive policy on nnode metrics with budget B. 1
On Maximum Coverage in the Streaming Model & Application to Multitopic BlogWatch
"... We generalize the graph streaming model to hypergraphs. In this streaming model, hyperedges are arriving online and any computation has to be done onthefly using a small amount of space. Each hyperedge can be viewed as a set of elements (nodes), so we refer to our proposed model as the “setstream ..."
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We generalize the graph streaming model to hypergraphs. In this streaming model, hyperedges are arriving online and any computation has to be done onthefly using a small amount of space. Each hyperedge can be viewed as a set of elements (nodes), so we refer to our proposed model as the “setstreaming ” model of computation. We consider the problem of “maximum coverage”, in which k sets have to be selected that maximize the total weight of the covered elements. In the setstreaming model of computation, we show that our algorithm for maximumcoverage achieves an approximation factor of 1 4. When multiple passes are allowed, we also provide a Θ(log n) approximation algorithm for the setcover. We next consider a multitopic blogwatch application, an extension of blogalert like applications for handling simultaneous multipletopic requests. We show how the problems of maximumcoverage and setcover in the setstreaming model can be utilized to give efficient online solutions to this problem. We verify the effectiveness of our methods both on synthetic and real weblog data. 1
Sequential Learning for Optimal Monitoring of Multichannel Wireless Networks
"... Abstract—We consider the problem of optimally assigning p sniffers to K channels to monitor the transmission activities in a multichannel wireless network. The activity of users is initially unknown to the sniffers and is to be learned along with channel assignment decisions while maximizing the be ..."
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Abstract—We consider the problem of optimally assigning p sniffers to K channels to monitor the transmission activities in a multichannel wireless network. The activity of users is initially unknown to the sniffers and is to be learned along with channel assignment decisions while maximizing the benifits of this assignment, resulting in the fundamental tradeoff between exploration versus exploitation. We formulate it as the linear partial monitoring problem, a superclass of multiarmed bandits. As the number of arms (snifferchannel assignments) is exponential, novel techniques are called for, to allow efficient learning. We use the linear bandit model to capture the dependency amongst the arms and develop two policies that take advantage of this dependency. Both policies enjoy logarithmic regret bound of timeslots with a term that is sublinear in the number of arms. I.
Approximating minimumpower degree and connectivity problems
 In LATIN
, 2008
"... Abstract Power optimization is a central issue in wireless network design. Given a (possibly directed) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless n ..."
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Cited by 8 (6 self)
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Abstract Power optimization is a central issue in wireless network design. Given a (possibly directed) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider several fundamental undirected network design problems under the power minimization criteria. Given a graphG
Submodularity and curvature: the optimal algorithm
"... Let (X, I) be a matroid and let f: 2 X → R+ be a monotone submodular function. The curvature of f is a parameter c ∈ [0, 1] such that for any S ⊂ X and j ∈ X \ S, f(S ∪ {j}) − f(S) ≥ (1 − c)f({j}). We consider the optimization problem max{f(S) : S ∈ I}. It is known that the greedy algorithm yields ..."
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Cited by 7 (1 self)
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Let (X, I) be a matroid and let f: 2 X → R+ be a monotone submodular function. The curvature of f is a parameter c ∈ [0, 1] such that for any S ⊂ X and j ∈ X \ S, f(S ∪ {j}) − f(S) ≥ (1 − c)f({j}). We consider the optimization problem max{f(S) : S ∈ I}. It is known that the greedy algorithm yields a 1/2approximation for this problem [11], and 1approximation when f has curvature c [4]. For the uniform matroid, it was known 1+c that the greedy algorithm yields an improved 1 c (1 − e−c)approximation [4]. In this paper, we analyze the continuous greedy algorithm [23] and prove that it gives a 1 c (1 − e−c)approximation for any matroid. Moreover, we show that this holds for a relaxed notion of curvature, curvature with respect to the optimum, and we prove that any better approximation under these conditions would require an exponential number of value queries.
Optimizing Multicast Performance in LargeScale WLANs
 in IEEE ICDCS
, 2007
"... Support for efficient multicasting in WLANs can enable new services such as streaming TV channels, radio channels, and visitor’s information. With increasing deployments of largescale WLANs, such services can have a significant impact. However, for a solution to be viable, the mutlicast services mu ..."
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Cited by 6 (3 self)
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Support for efficient multicasting in WLANs can enable new services such as streaming TV channels, radio channels, and visitor’s information. With increasing deployments of largescale WLANs, such services can have a significant impact. However, for a solution to be viable, the mutlicast services must minimally impact the existing unicast services which are currently the core services offered by most WLANs. This paper focuses on three objective functions motivated by different revenue functions and network scenarios: maximizing the number of users (MNU), balancing the load among APs (BLA), and minimizing the load of APs (MLA). We show that these problems are NPhard and present centralized approximation algorithms and distributed approaches to solve them. Using simulations we evaluate the performance of these algorithms. We observe that the number of users can be increased by up to 36.9%, and the maximum AP load and the total load can be reduced by up to 52.9 % and 31.1%, respectively. 1
Optimal monitoring in multichannel multiradio wireless mesh networks
 in MobiHoc. ACM, 2009
"... Wireless mesh networks (WMN) are finding increasing usage in citywide deployments for providing network connectivity. Mesh routers in WMNs typically use multiple wireless channels to enhance the spatialreuse of frequency bands, often with multiple radios per node. Due to the cooperative nature o ..."
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Wireless mesh networks (WMN) are finding increasing usage in citywide deployments for providing network connectivity. Mesh routers in WMNs typically use multiple wireless channels to enhance the spatialreuse of frequency bands, often with multiple radios per node. Due to the cooperative nature of WMNs, they are susceptible to many attacks that cannot be defeated by using traditional cryptographic mechanisms of authentication or encryption alone. A solution approach commonly used for defending against such attacks is behaviorbased detection in which some nodes overhear communication in their neighborhood to determine if the behavior by a neighbor is legitimate. It has been proposed to use specialized monitoring nodes deployed strategically throughout the network for performing such detection. The problem that arises is where to deploy these monitoring nodes, how to minimize their number, and which channels to tune their radios to, such that the maximum part of the network can be covered. This problem has been solved for single channel networks by a greedy approximation algorithm since the exact solution is NPhard. The greedy algorithm achieves the best performance, in terms of the worst case, possible among all polynomialtime algorithms provided that P 6 = NP. In this paper, we solve the problem for multichannel multiradio WMNs. The intuitive extension of the greedy algorithm destroys the property of best performance. Instead, we formulate the problem as an integer linear program, solve its linear program relaxation, and then use two rounding techniques that we develop by adapting existing rounding schemes. We thereby present two approximation algorithms. The first, computationallylight algorithm, called probabilistic rounding algorithm gives an expected best performance in the worst case. The second, called deterministic rounding algorithm achieves the best worstcase performance in a deterministic manner. To evaluate how the three algorithms perform in practice, we simulate them in random networks and scalefree networks.
A survey on algorithmic approaches for solving tourist trip design problems
 J. Heuristics
, 2014
"... The tourist trip design problem (TTDP) refers to a routeplanning problem for tourists interested in visiting multiple points of interest (POIs). TTDP solvers derive daily tourist tours, i.e., ordered visits to POIs, which respect tourist constraints and POIs attributes. The main objective of the pr ..."
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The tourist trip design problem (TTDP) refers to a routeplanning problem for tourists interested in visiting multiple points of interest (POIs). TTDP solvers derive daily tourist tours, i.e., ordered visits to POIs, which respect tourist constraints and POIs attributes. The main objective of the problem discussed is to select POIs that match tourist preferences, thereby maximizing tourist satisfaction, while taking into account a multitude of parameters and constraints (e.g., distances among POIs, visiting time required for each POI, POIs visiting days/hours, entrance fees, weather conditions) and respecting the time available for sightseeing on a daily basis. The aim of this work is to survey models, algorithmic approaches and methodologies concerning tourist trip design problems. Recent approaches are examined, focusing on problem models that best capture a multitude of realistic POIs attributes and user constraints; further, several interesting TTDP variants are investigated. Open issues and promising prospects in tourist trip planning research are also discussed. 1
Paths, trees and minimum latency tours
 Proc. of FOCS
, 2003
"... We give improved approximation algorithms for a variety of latency minimization problems. In particular, we give a 3.59 1approximation to the minimum latency problem, improving on previous algorithms by a multiplicative factor of 2. Our techniques also give similar improvements for related problems ..."
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We give improved approximation algorithms for a variety of latency minimization problems. In particular, we give a 3.59 1approximation to the minimum latency problem, improving on previous algorithms by a multiplicative factor of 2. Our techniques also give similar improvements for related problems like ktraveling repairmen and its multiple depot variant. We also observe that standard techniques can be used to speed up the previous and this algorithm by a factor of Õ(n). 1