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53
Efficient Informative Sensing using Multiple Robots
"... The need for efficient monitoring of spatio-temporal 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 ..."
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Cited by 56 (5 self)
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The need for efficient monitoring of spatio-temporal 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 near-optimally solving the NP-hard optimization problem of planning such informative paths. In particular, we first develop eSIP (efficient Single-robot 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 multi-robot problem. This procedure approximately generalizes any guarantees for the single-robot problem to the multi-robot case. We extensively evaluate the effectiveness of our approach on several experiments performed in-field for two important environmental sensing applications, lake and river monitoring, and simulation experiments performed using several real world sensor network data sets. 1.
Automatic Construction of Travel Itineraries using Social Breadcrumbs
"... Vacation planning is one of the frequent—but nonetheless laborious—tasks that people engage themselves with online; requiring skilled interaction with a multitude of resources. This paper constructs intra-city travel itineraries automatically by tapping a latent source reflecting geo-temporal breadc ..."
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Cited by 26 (0 self)
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Vacation planning is one of the frequent—but nonetheless laborious—tasks that people engage themselves with online; requiring skilled interaction with a multitude of resources. This paper constructs intra-city travel itineraries automatically by tapping a latent source reflecting geo-temporal breadcrumbs left by millions of tourists. For example, the popular rich media sharing site, Flickr, allows photos to be stamped by the time of when they were taken and be mapped to Points Of Interests (POIs) by geographical (i.e. latitudelongitude) and semantic (e.g., tags) metadata. Leveraging this information, we construct itineraries following a two-step approach. Given a city, we first extract photo streams of individual users. Each photo stream provides estimates on where the user was, how long he stayed at each place, and what was the transit time between places. In the second step, we aggregate all user photo streams into a POI graph. Itineraries are then automatically constructed from the graph based on the popularity of the POIs and subject to the user’s time and destination constraints. We evaluate our approach by constructing itineraries for several major cities and comparing them, through a“crowdsourcing” marketplace (Amazon Mechanical Turk), against itineraries constructed from popular bus tours that are professionally generated. Our extensive survey-based user studies over about 450 workers on AMT indicate that high quality itineraries can be automatically constructed from Flickr data.
Nonmyopic Adaptive Informative Path Planning for Multiple Robots
"... Many robotic path planning applications, such as search and rescue, involve uncertain environments with complex dynamics that can be only partially observed. When selecting the best subset of observation locations subject to constrained resources (such as limited time or battery capacity) it is an i ..."
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Cited by 17 (1 self)
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Many robotic path planning applications, such as search and rescue, involve uncertain environments with complex dynamics that can be only partially observed. When selecting the best subset of observation locations subject to constrained resources (such as limited time or battery capacity) it is an important problem to trade off exploration (gathering information about the environment) and exploitation (using the current knowledge about the environment most effectively) for efficiently observing these environments. Even the nonadaptive setting, where paths are planned before observations are made, is NP-hard, and has been subject to much research. In this paper, we present a novel approach to adaptive informative path planning that addresses this exploration-exploitation tradeoff. Our approach is nonmyopic, i.e. it plans ahead for possible observations that can be made in the future. We quantify the benefit of exploration through the “adaptivity gap ” between an adaptive and a nonadaptive algorithm in terms of the uncertainty in the environment. Exploiting the submodularity (a diminishing returns property) and locality properties of the objective function, we develop an algorithm that performs provably near-optimally in settings where the adaptivity gap is small. In case of large gap, we use an objective function that simultaneously optimizes paths for exploration and exploitation. We also provide an algorithm to extend any single robot algorithm for adaptive informative path planning to the multi robot setting while approximately preserving the theoretical guarantee of the single robot algorithm. We extensively evaluate our approach on a search and rescue domain and a scientific monitoring problem using a real robotic system.
Poly-logarithmic approximation algorithms for Directed Vehicle Routing Problems
- Proc. of APPROX
, 2007
"... Abstract. This paper studies vehicle routing problems on asymmetric metrics. Our starting point is the directed k-TSP problem: given an asymmetric metric (V, d), a root r ∈ V and a target k ≤ |V |, compute the minimum length tour that contains r and at least k other vertices. We present a polynomial ..."
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Cited by 14 (2 self)
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Abstract. This paper studies vehicle routing problems on asymmetric metrics. Our starting point is the directed k-TSP problem: given an asymmetric metric (V, d), a root r ∈ V and a target k ≤ |V |, compute the minimum length tour that contains r and at least k other vertices. We present a polynomial time O(log 2 n · log k)-approximation algorithm for this problem. We use this algorithm for directed k-TSP to obtain an O(log 2 n)-approximation algorithm for the directed orienteering problem. This answers positively, the question of poly-logarithmic approximability of directed orienteering, an open problem from Blum et al. [2]. The previously best known results were quasi-polynomial time algorithms with approximation guarantees of O(log 2 k) for directed k-TSP, and O(log n) for directed orienteering (Chekuri & Pal [4]). Using the algorithm for directed orienteering within the framework of Blum et al. [2] and Bansal et al. [1], we also obtain poly-logarithmic approximation algorithms for the directed versions of discounted-reward TSP and the vehicle routing problem with time-windows. 1
Approximation algorithms for the traveling repairman and speeding deliveryman problems with unit-time windows
- In APPROX-RANDOM, volume 4627 of LNCS
, 2007
"... Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits the maximum possible number of locations during their time w ..."
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Cited by 12 (1 self)
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Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits the maximum possible number of locations during their time windows. In the second variation, the speeding deliveryman problem, the goal is to find a tour that uses the minimum possible speedup to visit all locations during their time windows. For both variations, the time windows are of unit length, and the distance metric is based on a weighted, undirected graph. Algorithms with improved approximation ratios are given for the case when the input is defined on a tree rather than a general graph. The algorithms are also extended to handle time windows whose lengths fall in any bounded range. 1
Interactive Itinerary Planning
"... Planning an itinerary when traveling to a city involves substantial effort in choosing Points-of-Interest (POIs), deciding in which order to visit them, and accounting for the time it takes to visit each POI and transit between them. Several online services address different aspects of itinerary pla ..."
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Cited by 12 (2 self)
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Planning an itinerary when traveling to a city involves substantial effort in choosing Points-of-Interest (POIs), deciding in which order to visit them, and accounting for the time it takes to visit each POI and transit between them. Several online services address different aspects of itinerary planning but none of them provides an interactive interface where users give feedbacks and iteratively construct their itineraries based on personal interests and time budget. In this paper, we formalize interactive itinerary planning as an iterative process where, at each step: (1) the user provides feedback on POIs selected by the system, (2) the system recommends the best itineraries based on all feedback so far, and (3) the system further selects a new set of POIs, with optimal utility, to solicit feedback for, at the next step. This iterative process stops when the user is satisfied with the recommended itinerary. We show that computing an itinerary is NP-complete even for simple itinerary scoring functions, and that POI selection is NP-complete. We develop heuristics and optimizations for a specfic case where the score of an itinerary is proportional to the number of desired POIs it contains. Our extensive experiments show that our algorithms are efficient and return high quality itineraries. Abstract — 1 I.
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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Cited by 12 (4 self)
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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 constant-factor approximation algorithm for the best non-adaptive policy for the Stochastic Orienteering problem. We also show a small adaptivity gap—i.e., the existence of a non-adaptive 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 non-adaptive policy which is an O(lognlogB)-approximation to the best adaptive policy on n-node metrics with budget B. 1
Robust Sensor Placements at Informative and Communication-Efficient Locations
, 2010
"... 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 data-driven approach that addresses the three ..."
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Cited by 10 (0 self)
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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 data-driven approach that addresses the three central aspects of this problem: measuring the predictive quality of a set of hypothetical sensor locations, predicting the communication cost involved with these placements, and designing an algorithm with provable quality guarantees that optimizes the NP-hard tradeoff. Specifically, we use data from a pilot deployment to build non-parametric 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, polynomial-time, data-driven algorithm, PSPIEL, which selects Sensor Placements at Informative and communication-Efficient Locations. Our approach exploit two important properties of this problem: submodularity, formalizing the intuition that adding a node to a small deployment can help more than adding it 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 approach. We also show how our placements can be made robust against changes in the environment,
Approximation Algorithms for the Directed k-Tour and k-Stroll Problems
"... We consider two natural generalizations of the Asymmetric Traveling Salesman problem: the k-Stroll and the k-Tour problems. The input to the k-Stroll problem is a directed n-vertex graph with nonnegative edge lengths, an integer k, and two special vertices s and t. The goal is to find a minimum-leng ..."
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Cited by 10 (1 self)
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We consider two natural generalizations of the Asymmetric Traveling Salesman problem: the k-Stroll and the k-Tour problems. The input to the k-Stroll problem is a directed n-vertex graph with nonnegative edge lengths, an integer k, and two special vertices s and t. The goal is to find a minimum-length s-t walk, containing at least k distinct vertices. The k-Tour problem can be viewed as a special case of k-Stroll, where s = t. That is, the walk is required to be a tour, containing some pre-specified vertex s. When k = n, the k-Stroll problem becomes equivalent to Asymmetric Traveling Salesman Path, and k-Tour to Asymmetric Traveling Salesman. Our main result is a polylogarithmic approximation algorithm for the k-Stroll problem. Prior to our work, only bicriteria (O(log 2 k), 3)-approximation algorithms have been known, producing walks whose length is bounded by 3OPT, while the number of vertices visited is Ω(k / log 2 k). We also show a simple O(log 2 n / log log n)-approximation algorithm for the k-Tour problem. The best previously known approximation algorithms achieved min(O(log 3 k), O(log 2 n · log k / log log n))-approximation in polynomial time, and O(log 2 k)-approximation in quasipolynomial time. 1
