S Ravi Kumar

Cornell University, Ithaca, New York, United States

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Publications (9)5.49 Total impact

  • Bruno Codenotti · Funda Ergün · Peter Gemmell · S. Ravi Kumar
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    ABSTRACT: In this paper we show how to construct efficient checkers for programs that supposedly compute properties of polynomials. The properties we consider are roots, norms, and other analytic/algebraic functions of polynomials. In our model, both the program II and the polynomial p are available to the checker each as a black box. We show how to check programs that compute a specific root (e.g., the largest) or a subset of roots of the given polynomial. The checkers, in addition to never computing the root(s) themselves, strive to minimize both the running time (preferably o(deg2 p)) and the number of black box evaluations of p (preferably o(degp)). We obtain deterministic checkers when a separation bound between the roots is known and probabilistic checkers when the roots can be arbitrarily close. We then extend the checkers to handle the situations when the program II returns an approximation to the root and when the evaluation of the polynomial p is approximate. Our results translate into efficient checkers for matrix spectra computations both in the exact and approximate settings, operating in the library model of [BLR93]. Next we show that the usual characterization of norms using the triangle inequality is not suited for self-testing in the exact case, but surprisingly, could be used in the approximate case. Our results are complementary to most of the existing results on testing polynomials. The testers in the latter have the goal of determining whether a program computes a polynomial of given degree, whereas we are interested in checking the properties of a given polynomial.
    No preview · Chapter · Nov 2006
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    Funda Ergun · S Ravi Kumar · Ronitt Rubinfeld
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    ABSTRACT: We introduce a new model of distributions generated by random walks on graphs. This model suggests a variety of learning problems, using the definitions and models of distribution learning defined in [6]. Our framework is general enough to model previously studied distribution learning problems, as well as to suggest new applications. We describe special cases of the general problem, and investigate their relative difficulty. We present algorithms to solve the learning problem under various conditions. 1 INTRODUCTION In this paper, we introduce a new model of distributions generated by random walks on graphs. This model suggests a variety of learning problems, using the definitions and models of distribution learning defined by Kearns et. al. [6]. Our framework is general enough to model various noise processes, the Hamming ball distribution learning problem studied by [6], and the evolutionary tree model studied by Farach and Kannan [2]. Other possible applications to prob...
    Preview · Article · Dec 2000
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    ABSTRACT: On Labor Day weekend, the highway patrol sets up spot-checks at random points on the freeways with the intention of deterring a large fraction of motorists from driving incorrectly. We explore a very similar idea in the context of program checking to ascertain with minimal overhead that a program output is reasonably correct. Our model of spot-checking requires that the spot-checker must run asymptotically much faster than the combined length of the input and output. We then show that the spot-checking model can be applied to problems in a wide range of areas, including problems regarding graphs, sets, and algebra. In particular, we present spot-checkers for sorting, convex hull, element distinctness, set containment, set equality, total orders, and correctness of group and field operations. All of our spot-checkers are very simple to state and rely on testing that the input and/or output have certain simple properties that depend on very few bits. Our results also give property tests as defined by Rubinfeld and Sudan (1996, SIAM J. Comput. 25, 252–271), Rubinfeld (1994, “Proc. 35th Foundations of Computer Science,” pp. 288–299), and Goldreich et al. (1998, J. Assoc. Comput. Mach. 45, 653–750). Copyright 2000 Academic Press.
    Preview · Article · May 2000 · Journal of Computer and System Sciences
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    Jing Huang · S Ravi Kumar · Mandar Mitra · Wei-jing Zhu · Ramin Zabih
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    ABSTRACT: We define a new image feature called the color correlogram and use it for image indexing and comparison. This feature distills the spatial correlation of colors and when computed efficiently, turns out to be both effective and inexpensive for content-based image retrieval. The correlogram is robust in tolerating large changes in appearance and shape caused by changes in viewing position, camera zoom, etc. Experimental evidence shows that this new feature outperforms not only the traditional color histogram method but also the recently proposed histogram refinement methods for image indexing/retrieval. We also provide a technique to cut down the storage requirement of the correlogram so that it is the same as that of histograms, with only negligible performance penalty compared to the original correlogram. We also suggest the use of color correlogram as a generic indexing tool to tackle various problems arising from image retrieval and video browsing. We adapt the correlogram to handle the problems of image subregion querying, object localization, object tracking, and cut detection. Experimental results again suggest that the color correlogram is more effective than the histogram for these applications, with insignificant additional storage or processing cost.
    Preview · Article · Jan 2000 · International Journal of Computer Vision
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    Jing Huang · S Ravi Kumar · Mandar Mitra
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    ABSTRACT: The paper addresses how relevance feedback can be used to improve the performance of content-based image retrieval. We present two supervised learning methods: learning the query and learning the metric. We combine the learning methods with the recently proposed color correlograms for image indexing/retrieval. Our results on a large image database of over 20; 000 images suggest that these learning methods are quite effective for content-basedimage retrieval. INTRODUCTION The recent explosion in Internet usage and the rapidly growing availability of multimedia resources on the World-Wide Web has created a demand for effective and flexible techniques for automatic image retrieval and video browsing [3, 8, 11, 1, 10]. Users need high-quality image retrieval (IR) systems in order to find useful images from the masses of electronically available digital image data. In a typical IR system, a user poses a query by providing an existing image (or creating one by drawing), and the system retr...
    Preview · Article · Sep 1997
  • Jing Huang · S. Ravi Kumar · M. Mitra · Wei-jing Zhu · R. Zabih
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    ABSTRACT: We define a new image feature called the color correlogram and use it for image indexing and comparison. This feature distills the spatial correlation of colors, and is both effective and inexpensive for content-based image retrieval. The correlogram robustly tolerates large changes in appearance and shape caused by changes in viewing positions, camera zooms, etc. Experimental evidence suggests that this new feature outperforms not only the traditional color histogram method but also the recently proposed histogram refinement methods for image indexing/retrieval
    No preview · Conference Paper · Jul 1997
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    ABSTRACT: Bandwidth is a very valuable resource in wavelength division multiplexed optical networks. The problem of finding an optimal assignment of wavelengths to requests is of fundamental importance in bandwidth utilization. We present a polynomial-time algorithm for this problem on fixed constant-size topologies. We combine this algorithm with ideas from Raghavan and Upfal (1994) to obtain an optimal assignment of wavelengths on constant degree undirected trees. Mihail, Kaklamanis, and Rao (1995) posed the following open question: what is the complexity of this problem on directed trees? We show that it is NP-complete both on binary and constant depth directed trees.
    Preview · Article · Jun 1997 · Information Processing Letters
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    Jing Huang · S Ravi Kumar · Mandar Mitra · Wei-jing Zhu · Ramin Zabih
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    ABSTRACT: We define a new image feature called the color correlogram and use it for image indexing and comparison. This feature distills the spatial correlation of colors, and is both effective and inexpensive for content-based image retrieval. The correlogramrobustly tolerates large changesin appearance and shape caused by changes in viewing positions, camera zooms, etc. Experimental evidence suggests that this new feature outperforms not only the traditional color histogram method but also the recently proposed histogram refinement methods for image indexing/retrieval. 1. Introduction With the rapid proliferation of the internet and the worldwide -web, the amount of digital image data accessible to users has grown enormously. Image databases are becoming larger and more widespread, and there is a growing need for effective and efficient image retrieval (IR) systems. Most IR systems adopt the following two-step approach to search image databases: (i) (indexing) for each image in a database,...
    Full-text · Article · May 1997
  • Funda Ergun · S.Ravi Kumar · Ronitt Rubinfeld
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    ABSTRACT: The authors show how to check programs that compute polynomials and functions defined by addition theorems-in the realistic setting where the output of the program is approximate instead of exact. They present results showing how to perform approximate checking, self-testing, and self-correcting of polynomials, settling in the affirmative a question raised by Gemmell et al. (1991), and Rubinfeld and Sudan (1992, 1996). They then show how to perform approximate checking, self-testing, and self-correcting for those functions that satisfy addition theorems, settling a question raised by Rubinfeld (1994]) In both cases, they show that the properties used to test programs for these functions are both robust (in the approximate sense) and stable. Finally, they explore the use of reductions between functional equations in the context of approximate self-testing. Their results have implications to the stability theory of functional equations
    No preview · Conference Paper · Nov 1996