## Khanna, Sanjeev

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Publication Randomized Pursuit-Evasion With Limited Visibility(2003-01-01) Kannan, Sampath; Isler, Volkan; Khanna, SanjeevWe study the following pursuit-evasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters suffice for catching rabbits with such local visibility with high probability. We distinguish between reactive rabbits who move only when a hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunter-win, that is, if a single hunter can capture a rabbit of either kind on G.Publication A PTAS for Minimizing Average Weighted Completion Time With Release Dates on Uniformly Related Machines(2000-01-01) Chekuri, Chandra; Khanna, SanjeevA classical scheduling problem is to find schedules that minimize average weighted completion time of jobs with release dates. When multiple machines are available, the machine environments may range from identical machines (the processing time required by a job is invariant across the machines) at one end, to unrelated machines (the processing time required by a job on any machine is an arbitrary function of the specific machine) at the other end of the spectrum. While the problem is strongly NP-hard even in the case of a single machine, constant factor approximation algorithms have been known for even the most general machine environment of unrelated machines. Recently, a polynomial-time approximation scheme (PTAS) was discovered for the case of identical parallel machines [1]. In contrast, it is known that this problem is MAX SNP-hard for unrelated machines [10]. An important open problem is to determine the approximability of the intermediate case of uniformly related machines where each machine i has a speed si and it takes p/si time to executing a job of processing size pIn this paper, we resolve this problem by obtaining a PTAS for the problem. This improves the earlier known ratio of (2 + ∈) for the problem.Publication Preserving Module Privacy in Workflow Provenance(2010-05-28) Davidson, Susan B; Khanna, Sanjeev; Panigrahi, Debmalya; Roy, SudeepaWe study the problem of providing workflow data provenance without revealing the functionality of any module. We develop a model that formalizes the notion of privacy of modules embedded in a workflow structure as a natural extension of privacy of standalone modules. Our model shows that by hiding a small amount of carefully chosen data, one can ensure privacy of all modules over an unbounded number of executions. The problem of identifying the smallest possible amount of such data is NP-hard, and in the full generality of our model it is in fact even hard to get a good approximation. However, we are able to design good approximation algorithms for optimizing the amount of hidden data when either the privacy model is slighted restricted or there is bounded sharing of data items among various modules.Publication Target Tracking With Distributed Sensors: The Focus of Attention Problem(2003-01-01) Isler, Volkan; Khanna, Sanjeev; Spletzer, John; Taylor, Camillo JIn this paper, we investigate data fusion techniques for target tracking using distributed sensors. Specifically, we are interested in how pairs of bearing or range sensors can be best assigned to targets in order to minimize the expected error in the estimates. We refer to this as the focus of attention (FOA) problem. In its general form, FOA is NP-hard and not well approximable. However, for specific geometries we obtain significant approximation results: a 2-approximation algorithm for stereo cameras on a line, a PTAS for when the cameras are equidistant, and a 1.42 approximation for equally spaced range sensors on a circle. In addition to constrained geometries, we further investigate the problem for general sensor placement. By reposing as a maximization problem -- where the goal is to maximize the number of tracks with bounded error -- we are able to leverage results from maximum set-packing to render the problem approximable. We demonstrate these in simulation for a target tracking task, and for localizing a team of mobile agents in a sensor network. These results provide insights into sensor/target assignment strategies, as well as sensor placement in a distributed network.Publication Target Tracking with Distributed Sensors: The Focus of Attention Problem(2003-10-27) Isler, Volkan; Khanna, Sanjeev; Spletzer, John R.; Taylor, Camillo JIn this paper, we investigate data fusion techniques for target tracking using distributed sensors. Specifically, we are interested in how pairs of bearing or range sensors can be best assigned to targets in order to minimize the expected error in the estimates. We refer to this as the focus of attention (FOA) problem. In its general form, FOA is NP-hard and not well approximable. However, for specific geometries we obtain significant approximation results: a 2-approximation algorithm for stereo cameras on a line, a PTAS for when the cameras are equidistant, and a 1.42 approximation for equally spaced range sensors on a circle. By reposing as a maximization problem - where the goal is to maximize the number of tracks with bounded error - we are able to leverage results from maximum set-packing to render the problem approximable. We demonstrate the results in simulation for a target tracking task, and for localizing a team of mobile agents in a sensor network. These results provide insights into sensor/target assignment strategies, as well as sensor placement in a distributed network.Publication Enabling Privacy in Provenance-Aware Workflow Systems(2011-01-01) Davidson, Susan B; Khanna, Sanjeev; Stoyanovich, Julia; Tannen, Val; Roy, Sudeepa; Chen, Yi; Milo, TovaPublication Power-Conserving Computation of Order-Statistics over Sensor Networks(2004-06-14) Greenwald, Michael B; Khanna, SanjeevWe study the problem of power-conserving computation of order statistics in sensor networks. Significant power-reducing optimizations have been devised for computing simple aggregate queries such as COUNT, AVERAGE, or MAX over sensor networks. In contrast, aggregate queries such as MEDIAN have seen little progress over the brute force approach of forwarding all data to a central server. Moreover, battery life of current sensors seems largely determined by communication costs - therefore we aim to minimize the number of bytes transmitted. Unoptimized aggregate queries typically impose extremely high power consumption on a subset of sensors located near the server. Metrics such as total communication cost underestimate the penalty of such imbalance: network lifetime may be dominated by the worst-case replacement time for depleted batteries. In this paper, we design the first algorithms for computing order-statistics such that power consumption is balanced across the entire network. Our first main result is a distributed algorithm ε-approximate quantile summary of the sensor data such that each sensor transmits only O(log2n/ε) data values, irrespective of the network topology, an improvement over the current worst-case behavior of Ω(n). Second, we show an improved result when the height, h, of the network is significantly smaller than n. Our third result is that we can exactly compute any order statistic (e.g., median) in a distributed manner such that each sensor needs to transmit O(log3n) values. Further, we design the aggregates used by our algorithms to be decomposable. An aggregate Q over a set S is decomposable if there exists a function, f, such that for all S = S1 ∪ S2, Q(S) = f(Q(S1),Q(S2)). We can thus directly apply existing optimizations to decomposable aggregates that inrease error-resilience and reduce communication cost. Finally, we validate our results empirically, through simulation. When we compute the median exactly, we show that, even for moderate size networks, the worst communication cost for any single node is several times smaller than the corresponding cost in prior median algorithms. We show similar cost reductions when computing approximate order-statistic summaries with guaranteed precision. In all cases, our total communication cost over the entire network is smaller than or equal to the total cost of prior algorithms.Publication Optimal Lower Bounds for Universal and Differentially Private Steiner Trees and TSPs(2011-08-01) Bhalgat, Anand; Chakrabarty, Deeparnab; Khanna, SanjeevGiven a metric space on n points, an !-approximate universal algorithm for the Steiner tree problem outputs a distribution over rooted spanning trees such that for any subset X of vertices containing the root, the expected cost of the induced subtree is within an a factor of the optimal Steiner tree cost for X. An a-approximate differentially private algorithm for the Steiner tree problem takes as input a subset X of vertices, and outputs a tree distribution that induces a solution within an a factor of the optimal as before, and satisfies the additional property that for any set X' that differs in a single vertex from X, the tree distributions for X and X' are “close” to each other. Universal and differentially private algorithms for TSP are defined similarly. An a-approximate universal algorithm for the Steiner tree problem or TSP is also an a-approximate differentially private algorithm. It is known that both problems admit O(log n)-approximate universal algorithms, and hence O(log n) approximate differentially private algorithms as well. We prove an Ω(log n) lower bound on the approximation ratio achievable for the universal Steiner tree problem and the universal TSP, matching the known upper bounds. Our lower bound for the Steiner tree problem holds even when the algorithm is allowed to output a more general solution of a distribution on paths to the root. We then show that whenever the universal problem has a lower bound that satisfies an additional property, it implies a similar lower bound for the differentially private version. Using this converse relation between universal and private algorithms, we establish an Ω(log n) lower bound for the differentially private Steiner tree and the differentially private TSP. This answers a question of Talwar [19]. Our results highlight a natural connection between universal and private approximation algorithms that is likely to have other applications.Publication Why and Where: A Characterization of Data Provenance(2001-01-01) Buneman, Peter; Khanna, Sanjeev; Tan, Wang-ChiewWith the proliferation of database views and curated databases, the issue of data provenance - where a piece of data came from and the process by which it arrived in the database - is becoming increasingly important, especially in scientific databases where understanding provenance is crucial to the accuracy and currency of data. In this paper we describe an approach to computing provenance when the data of interest has been created by a database query. We adopt a syntactic approach and present results for a general data model that applies to relational databases as well as to hierarchical data such as XML. A novel aspect of our work is a distinction between "why" provenance (refers to the source data that had some influence on the existence of the data) and "where" provenance (refers to the location(s) in the source databases from which the data was extracted).Publication Social Welfare in One-Sided Matching Markets Without Money(2011-08-01) Bhalgat, Anand; Chakrabarty, Deeparnab; Khanna, SanjeevWe study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments.We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent’s utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation. We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526, 2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first non-trivial performance guarantees for these natural mechanisms.