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Desai A.,Indian Institute of Technology Kanpur | Desai A.,Tower Research Capital LLC | Jain E.,Indian Institute of Technology Kanpur | Roy S.,Indian Institute of Technology Kanpur
Proceedings - Asia-Pacific Software Engineering Conference, APSEC | Year: 2013

Generating invariants for loops is often a grueling obstacle in formal program verification. Researchers have employed methods from formal techniques based on abstract interpretation to test-driven dynamic analysis to tackle this problem. Even though powerful techniques for generating conjunctive invariants (invariants that employ only conjunction of terms) have been developed, disjunctive invariants have remained a sore thumb for formal techniques. In this paper, we propose a technique to transform certain category of loops, those that have a static iteration pattern, into loops that can be handled by conjunctive invariant generators. The key idea is to identify a static iteration pattern that distributes the disjunction in an invariant in a manner that can be captured by only conjunctive invariants. To broaden the scope of our algorithm, we also propose the idea of parametric verification, while attempting to verify specialized versions of the program where a subset of the input variables is instantiated with certain test-inputs. Note that parametric verification distinguishes it from program testing as testing requires all of its variables to be instantiated with test-inputs. We discuss our ideas on loops drawn from real programs to establish real-world applicability of our algorithms. © 2013 IEEE.

Geng Q.,Tower Research Capital LLC | Kairouz P.,University of Illinois at Urbana - Champaign | Oh S.,University of Illinois at Urbana - Champaign | Viswanath P.,University of Illinois at Urbana - Champaign
IEEE Journal on Selected Topics in Signal Processing | Year: 2015

Adding Laplacian noise is a standard approach in differential privacy to sanitize numerical data before releasing it. In this paper, we propose an alternative noise adding mechanism: the staircase mechanism, which is a geometric mixture of uniform random variables. The staircase mechanism can replace the Laplace mechanism in each instance in the literature and for the same level of differential privacy, the performance in each instance improves; the improvement is particularly stark in medium-low privacy regimes. We show that the staircase mechanism is the optimal noise adding mechanism in a universal context, subject to a conjectured technical lemma (which we also prove to be true for one and two dimensional data). © 2015 IEEE.

Aggarwal A.,Tower Research Capital LLC | Louis A.,Georgia Institute of Technology | Bansal M.,University of Delhi | Garg N.,Indian Institute of Technology Delhi | And 3 more authors.
Mathematical Programming | Year: 2013

We consider the facility location problem where each facility can serve at most U clients. We analyze a local search algorithm for this problem which uses only the operations of add, delete and swap and prove that any locally optimum solution is no more than 3 times the global optimum. This improves on a result of Chudak and Williamson who proved an approximation ratio of 3+2√ for the same algorithm. We also provide an example which shows that any local search algorithm which uses only these three operations cannot achieve an approximation guarantee better than 3. © 2012 Springer and Mathematical Optimization Society.

Geng Q.,Tower Research Capital LLC | Kannan S.,University of California at Berkeley | Viswanath P.,University of Illinois at Urbana - Champaign
IEEE Journal on Selected Areas in Communications | Year: 2014

We study interference channels (IFCs) where the interaction among sources and destinations is enabled, e.g., both sources and destinations can talk to each other using full-duplex radios. The interaction can come in two ways. First is through in-band interaction where sources and destinations can transmit and listen in the same channel simultaneously, enabling interaction. Second is through out-of-band interaction where destinations talk back to the sources on an out-of-band channel, which is possible from white-space channels. The flexibility afforded by the interaction among sources and destinations allows for the derivation of interference alignment (IA) strategies that have desirable 'engineering properties,' i.e., insensitivity to the rationality or irrationality of channel parameters, small block lengths, and finite SNR operations. We show that, for several classes of IFCs, the interactive IA scheme can achieve the optimal degrees of freedom. In particular, we show a simple scheme (having a finite block length for channels having no diversity) for three-user and four-user IFCs with full-duplex radios to achieve the optimal degrees of freedom even after accounting for the cost of interaction. On the technical side, we show using a Gröbner basis argument that, in a general network potentially utilizing cooperation and feedback, the optimal degrees of freedom under linear schemes of a fixed block length is the same for channel coefficients with a probability of 1. Furthermore, a numerical method to estimate this value is also presented. These tools have potentially wider utility in studying other wireless networks as well. © 1983-2012 IEEE.

Bai L.,Tower Research Capital LLC | Alexopoulos C.,Georgia Institute of Technology | Ferguson M.E.,University of South Carolina | Tsui K.-L.,Georgia Institute of Technology
Computers and Industrial Engineering | Year: 2012

Generally, the derivation of an inventory policy requires the knowledge of the underlying demand distribution. Unfortunately, in many settings demand is not completely observable in a direct way or inventory records may be inaccurate. A variety of factors, including the potential inaccuracy of inventory records, motivate managers to seek replenishment policies where the inventory is reviewed periodically and a fixed quantity Q is ordered once the inventory level is found to be under a certain point r. To apply such a policy, however, firms must derive the values r and Q without a clear understanding of the demand distribution. We develop estimators of the first two moments of the (periodic) demand by means of renewal theoretical concepts and a regression-based method, and use these estimators in conjunction with the Power Approximation (PA) method of Ehrhardt and Mosier (1984) to obtain an (r, Q) replenishment policy. The proposed methodology is robust and easy to code into a spreadsheet application. A series of numerical studies are carried out to evaluate the accuracy and precision of the estimators, and to investigate the impact of the estimation on the optimality of the inventory policies. Our experiments indicate that the proposed (r, Q) policy is very close, with regard to the expected total cost per period, to the (s, S) policy obtained via the PA method when the demand process is fully observable and inventory records are accurate.© 2012 Elsevier Ltd. All rights reserved.

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