]> dcg-ann.pdf Bernard Chazelle Benjamin Gum Alexey Lvov STOC 1999 5 This paper considers Approximate Nearest Neighbor Searching (ANNS), a basic problem of interest in a variety of areas ranging from molecular biology to data mining. Using ideas inspired by discrepancy theory, we establish the first query time lower bound on deterministic ANNS algorithms, even on a very special space -- the Hamming Cube -- and even if we require only very poor approximation. dcg-ann.pdf Bernard Chazelle Benjamin Gum Alexey Lvov Discrete and Computational Geometry: The Goodman-Pollack Festschrift, Springer-Verlag 2003 99 This paper considers Approximate Nearest Neighbor Searching (ANNS), a basic problem of interest in a variety of areas ranging from molecular biology to data mining. Using ideas inspired by discrepancy theory, we establish the first query time lower bound on deterministic ANNS algorithms, even on a very special space -- the Hamming Cube -- and even if we require only very poor approximation. sicomp-evasive.pdf Subhash Khot Yaoyun Shi STACS 2001 2 In this paper we present some partial answers to the famous conjecture that monotone graph properties are evasive. Adding new group theoretic and number theoretic ideas to a previously known topological method, we prove evasiveness of all minor-closed graph properties. We significantly improve known results for subgraph containment properties and for some generalizations. sicomp-evasive.pdf Subhash Khot Yaoyun Shi SIAM Journal on Computing 31(3) 2002 99 In this paper we present some partial answers to the famous conjecture that monotone graph properties are evasive. Adding new group theoretic and number theoretic ideas to a previously known topological method, we prove evasiveness of all minor-closed graph properties. We significantly improve known results for subgraph containment properties and for some generalizations. rsa-randglb.pdf Subhash Khot ICALP 2001 7 This paper considers the randomized decision tree complexity of monotone properties of graphs. We improve the previous best unconditional lower bound, using simple tools from probability theory. rsa-randglb.pdf Subhash Khot Random Structures and Algorithms 30(3) 2007 5 This paper considers the randomized decision tree complexity of monotone properties of graphs. We improve the previous best unconditional lower bound, using simple tools from probability theory. focs01-infocomplex.pdf Yaoyun Shi Anthony Wirth Andrew Yao FOCS 2001 10 not occur. We also prove some generalizations and extensions. ]]> ipco02-rap.pdf Gruia Calinescu Howard Karloff Yuval Rabani IPCO 2002 5 We consider the problem of selecting a maximum profit subset from a given set of jobs such that the total resource requirement at no point of time exceeds a given bound (this can be thought of as maximum throughput scheduling). We give the current best constant factor approximation. algorithmica-ufp.pdf Chandra Chekuri Anupam Gupta Amit Kumar APPROX 2002 9 This paper studies the problem of routing, through a network, a maximum profit subset of a given set of unsplittable flows, while respecting all edge capacity constraints. We improve some earlier results for expander networks and simplify others. We also obtain new results for the line and ring networks. algorithmica-ufp.pdf Chandra Chekuri Anupam Gupta Amit Kumar Algorithmica 47(1) 2007 2 This paper studies the problem of routing, through a network, a maximum profit subset of a given set of unsplittable flows, while respecting all edge capacity constraints. We improve some earlier results for expander networks and simplify others. We also obtain new results for the line and ring networks. ccc03-disj.pdf Subhash Khot Xiaodong Sun CCC (Complexity) 2003 7 Suppose each of t players is given as input a subset of {1,2...,n} with the promise that the t sets are either pairwise disjoint or have an element in common but are otherwise pairwise disjoint. How many bits of randomised communication are needed for them to distinguish between these two cases? We establish lower bounds for this problem that match the best known upper bounds, upto logarithmic factors. The above problem has connections with the computation of frequency moments for massive data in the streaming model. Our communication lower bounds imply space lower bounds in that model. http://eccc.hpi-web.de/eccc-reports/2003/TR03-070/index.html Oded Regev FOCS 2004 10 We consider the approximate nearest neighbour search (ANNS) problem on the d-dimensional Hamming cube. For polynomial storage and poly(d) word size, we show matching lower and upper bounds on the number of randomised queries required to solve ANNS. This closes a long line of research on this basic and important problem. Yuhang Wang Fillia Makedon ACM Multimedia 2004 10 Yuhang's page. ]]> imath-entropy-ds.pdf Khanh Do_Ba Shan Muthukrishnan STACS 2006 2 A stream of m tokens, taken from a universe of size n (m >> n), defines a empirical probability distribution. Several applications in databases and network security need to summarize such a distribution. Entropy and the related "entropy norm" are two such summaries and particularly important ones because entropy is central to information theory. In this work, we provide space-efficient (sublinear space) algorithms to estimate these two quantities and prove a space lower bound for estimation of the entropy norm. imath-entropy-ds.pdf Khanh Do_Ba Shan Muthukrishnan Internet Mathematics 3(1) 2006 99 A stream of m tokens, taken from a universe of size n (m >> n), defines a empirical probability distribution. Several applications in databases and network security need to summarize such a distribution. Entropy and the related "entropy norm" are two such summaries and particularly important ones because entropy is central to information theory. In this work, we provide space-efficient (sublinear space) algorithms to estimate these two quantities and prove a space lower bound for estimation of the entropy norm. stoc06-ufp-qptas.pdf Nikhil Bansal Amir Epstein Baruch Schieber STOC 2006 5 We study the problem of routing multicommodity network flows on a line network with non-uniform capacities and obtain a quasi-polynomial-time approximation scheme for the max profit routable subset of a given set of flow demands. Our algorithm also extends to ring networks. These results improve upon earlier (2+epsilon)-approximations. More importantly, they addresses the long-standing open question of whether or not this problem is APX-hard on lines and rings. Our results strongly indicate that it is not. kdd06-attack.pdf Sheng Zhang Fillia Makedon James Ford KDD 2006 8 Details will be posted here in due course; please stand by. Details will be posted here in due course; please stand by. Details will be posted here in due course; please stand by. talg-entropy-opt.pdf Graham Cormode Andrew McGregor SODA 2007 1 optimal algorithm and we prove this near-optimality via a lower bound. We also prove upper and lower bound results for estimating a related quantity called the kth order entropy. ]]> talg-entropy-opt.pdf Graham Cormode Andrew McGregor ACM Transactions on Algorithms (to appear) 2009 2 optimal algorithm and we prove this near-optimality via a lower bound. We also prove upper and lower bound results for estimating a related quantity called the kth order entropy. ]]> ccc07-mpj.pdf CCC (Complexity) 2007 6 In the pointer jumping problem, a number of players who share an input graph amongst themselves, must communicate to determine the node reached by following pointers (i.e., directed edges) out of a designated start node. This problem is considered a promising candidate for resolving some long-standing open problems in circuit complexity. Here, we make progress on these open problems by proving large communication lower bounds for pointer jumping in certain restricted models. The hope is that in future work the restrictions can be relaxed to the point where we can derive nontrivial circuit lower bounds. mfcs07-apir.pdf Anna Shubina MFCS 2007 8 Coming soon. Please stand by. soda08-median-ds.pdf T. S. Jayram Mihai Patrascu SODA 2008 1 We show that any algorithm computing the median of a stream presented in random order, using $\polylog(n)$ space, requires an optimal $\Omega(\log\log n)$ passes, resolving an open question from the seminal paper on streaming by Munro and Paterson, from FOCS 1978. stacs08-mpj-ub.pdf Joshua Brody STACS 2008 2 sublinear communication protocol. Proving strong lower bounds on MPJ is a long-standing challenge, and most techniques developed so far were shooting for linear lower bounds, and had succeeded in proving such lower bounds in somewhat restricted models. Our result therefore shows that there is something deep in the structure of MPJ that these earlier techniques cannot tackle. We also consider a new restricted model for MPJ (inspired by our upper bound) and prove a strong n - O(log n) lower bound in this model. ]]> stoc08-rcc.pdf Graham Cormode Andrew McGregor STOC 2008 5 Communication complexity typically involves partitioning the input to a problem amongst two (or more) players in a fixed way. But what happens if the data are instead partitioned at random amongst the players? When do traditionally hard problems become easy, and when do lower bounds stay robust? We initiate a study of such questions. A key motivation is that such random partition lower bounds apply quite directly to data stream lower bounds where the input is presented in random, rather than adversarial, order. focs08-planar.pdf Alexander Jaffe James Lee Justin Vincent FOCS 2008 10 Coming soon; please stand by. notyet.html Graham Cormode Andrew McGregor ICALP 2009 7 Coming soon; please stand by. submit-funcmon.pdf Chrisil Arackaparambil Joshua Brody ICALP 2009 7 Coming soon; please stand by. ccc09-ghd.pdf http://eccc.hpi-web.de/eccc-reports/2009/TR09-015/index.html http://arXiv.org/abs/0902.2399 Joshua Brody CCC 2009 7.5 Coming soon; please stand by. http://www.cs.dartmouth.edu/reports/abstracts/TR2009-642/ Chrisil Arackaparambil Chien-Chung Huang WADS 2009 3 Coming soon; please stand by.