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Alice and Bob would like to extract a common random string of min-entropy at least ... Keywords: hypercontractivity, communication complexity, covering codes, pseudorandomness, information theory, lower bounds 2 May 2016 IEEE Transactions on Information Theory: Volume 62 Issue 5, May 2016 Publisher: IEEE Press Bibliometrics: Citation Count: 1 We consider the problem of communication over a classical-quantum broadcast channel with one sender and two receivers. Generalizing the classical inner bounds shown by Marton and the recent quantum asymptotic version shown by Savov and Wilde, we obtain one-shot inner bounds in the quantum setting. Our bounds are stated in ... 3 January 2016 ITCS '16: Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 11,   Downloads (12 Months): 31,   Downloads (Overall): 104 Full text available: PDF We initiate the study of a quantity that we call coordination complexity. In a distributed optimization problem, the information defining a problem instance is distributed among n parties, who need to each choose an action, which jointly will form a solution to the optimization problem. The coordination complexity represents the ... Keywords: coordination complexity, privacy 4 January 2015 SODA '15: Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 2,   Downloads (12 Months): 11,   Downloads (Overall): 68 Full text available: PDF We consider the bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form "Is x in S ?" by adaptively ... Keywords: expansion, graphs of large girth, bit-probe model, compression, bloom filters, data structures 5 October 2014 FOCS '14: Proceedings of the 2014 IEEE 55th Annual Symposium on Foundations of Computer Science Publisher: IEEE Computer Society Bibliometrics: Citation Count: 6 We consider the communication cost of computing functions when inputs are distributed among the vertices of an undirected graph. The communication is assumed to be point-to-point: a processor sends messages only to its neighbors. The processors in the graph act according to a pre-determined protocol, which can be randomized and ... Keywords: Communication Complexity, Metric Embeddings, Distributed Computing 6 July 2013 Theoretical Computer Science: Volume 494, July, 2013 Publisher: Elsevier Science Publishers Ltd. Bibliometrics: Citation Count: 0 We study the complexity of the following problems in the streaming model. Membership testing forDLIN. We show that every language in DLIN can be recognized by a randomized one-pass O(logn) space algorithm with an inverse polynomial one-sided error and by a deterministic p-pass O(n/p) space algorithm. We show that these ... Keywords: Communication complexity, Context free language, Streaming algorithms, Randomized algorithms 7 October 2012 FOCS '12: Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science Publisher: IEEE Computer Society Bibliometrics: Citation Count: 2 We study the problem of constructing universal Steiner trees for undirected graphs. Given a graph $G$ and a root node $r$, we seek a single spanning tree $T$ of minimum {\em stretch}, where the stretch of $T$ is defined to be the maximum ratio, over all terminal sets $X$, of ... Keywords: universal Steiner tree, hierarchical graph partition, minor-free graphs, graph clustering 8 July 2012 ACM Transactions on Algorithms (TALG): Volume 8 Issue 3, July 2012 Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 1,   Downloads (12 Months): 11,   Downloads (Overall): 255 Full text available: PDF We show that some topologies arising naturally in the context of wireless networking are low-degree, expander graphs. Keywords: Bluetooth, Distributed algorithms, ad hoc networks, expander graphs, random key predistribution 9 August 2011 WADS'11: Proceedings of the 12th international conference on Algorithms and data structures Publisher: Springer-Verlag Bibliometrics: Citation Count: 3 We consider the problem of two-coloring n -uniform hypergraphs. It is known that any such hypergraph with at most 1/10√ n /ln n 2 n hyperedges can be two-colored [7]. In fact, there is an efficient (requiring polynomial time in the size of the input) randomized algorithm that produces such ... Keywords: property B, randomized algorithm, hypergraph coloring, streaming algorithm 10 September 2010 ESA'10: Proceedings of the 18th annual European conference on Algorithms: Part II Publisher: Springer-Verlag Bibliometrics: Citation Count: 1 We study the following set membership problem in the bit probe model: given a set S from a finite universe U , represent it in memory so that membership queries of the form "Is x in S ?" can be answered with a small number of bitprobes. We obtain explicit ... 11 July 2010 PODC '10: Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing Publisher: ACM Bibliometrics: Citation Count: 12 Downloads (6 Weeks): 2,   Downloads (12 Months): 3,   Downloads (Overall): 156 Full text available: PDF We consider a scenario where large data frames are broken into a few packets and transmitted over the network. Our focus is on a bottleneck router: the model assumes that in each time step, a set of packets (a burst) arrives, from which only one packet can be served, and ... Keywords: competitive analysis, multi-packet frames, online set packing, packet fragmentation 12 January 2010 IEEE Transactions on Information Theory: Volume 56 Issue 1, January 2010 Publisher: IEEE Press Bibliometrics: Citation Count: 3 We show combinatorial limitations on efficient list decoding of Reed-Solomon codes beyond the Johnson-Guruswami-Sudan bounds. In particular,we showthat for arbitrarily large fields F N , |F N | = N , for any δ Ɛ, (0,1) and K = N δ : • Existence: there exists a received word w ... Keywords: Johnson bound, list decoding, subspace polynomials, Guruswami–Sudan algorithm, Guruswami-Sudan algorithm, Reed–Solomon codes, Reed-Solomon codes 13 January 2010 IEEE Transactions on Information Theory: Volume 56 Issue 1, January 2010 Publisher: IEEE Press Bibliometrics: Citation Count: 9 Let X and Y be finite nonempty sets and (X,Y) a pair of random variables taking values in X × Y . We consider communication protocols between two parties, ALICE and BOB, for generating X and Y . ALICE is provided an x ∈ X generated according to the distribution ... Keywords: direct sum, mutual information, relative entropy, Communication complexity, communication complexity, rejection sampling 14 September 2009 Journal of the ACM (JACM): Volume 56 Issue 6, September 2009 Publisher: ACM Bibliometrics: Citation Count: 8 Downloads (6 Weeks): 3,   Downloads (12 Months): 25,   Downloads (Overall): 612 Full text available: PDF We prove the following information-theoretic property about quantum states. Substate theorem: Let ρ and σ be quantum states in the same Hilbert space with relative entropy S (ρ ‖ σ) ≔ Tr ρ (log ρ - log σ) = c . Then for all ϵ > 0, there is a ... Keywords: Privacy, quantum communication complexity, quantum information theory 15 June 2009 Algorithmica - Special Issue: Quantum Computation; Guest Editors: Frédéric Magniez and Ashwin Nayak: Volume 55 Issue 3, June 2009 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 4 We show that measuring any two low rank quantum states in a random orthonormal basis gives, with high probability, two probability distributions having total variation distance at least a universal constant times the Frobenius distance between the two states. This implies that for any finite ensemble of quantum states there ... Keywords: Ensemble quantum state distinction, Quantum Fourier transforms, Quantum algorithms, Gel’fand pairs, Frobenius distance, Hidden subgroup problem, Random orthonormal measurement bases 16 January 2009 SODA '09: Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithms Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 7 Downloads (6 Weeks): 2,   Downloads (12 Months): 6,   Downloads (Overall): 371 Full text available: PDF Given a data stream of length n over an alphabet [ m ] where n > m , we consider the problem of finding a duplicate in a single pass. We give a randomized algorithm for this problem that uses O ((log m ) 3 ) space. This answers a ... 17 October 2008 FOCS '08: Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science Publisher: IEEE Computer Society Bibliometrics: Citation Count: 1 We show a tight lower bound of $\Omega(N \log\log N)$ on the number oftransmissions required to compute several functions (including theparity function and the majority function) in a network of $N$randomly placed sensors, communicating using local transmissions, andoperating with power near the connectivity threshold. This resultconsiderably simplifies and strengthens an ... Keywords: lower bounds, wireless networks, broadcast protocols, sampling algorithms, noisy decision tree, average case lower bound 18 September 2008 SecureComm '08: Proceedings of the 4th international conference on Security and privacy in communication netowrks Publisher: ACM Bibliometrics: Citation Count: 2 Downloads (6 Weeks): 0,   Downloads (12 Months): 1,   Downloads (Overall): 64 Full text available: PDF We show that massive attacks against sensor networks that use random key pre-distribution schemes cannot be cheap, provided that the parameters are set in the right way. By choosing them appropriately, any adversary whose aim is to compromise a large fraction of the communication links is forced, with overwhelming probability, ... Keywords: security, random pre-distribution of keys, wireless sensor network 19 March 2008 ACM Transactions on Information and System Security (TISSEC): Volume 11 Issue 3, March 2008 Publisher: ACM Bibliometrics: Citation Count: 21 Downloads (6 Weeks): 2,   Downloads (12 Months): 11,   Downloads (Overall): 661 Full text available: PDF We give, for the first time, a precise mathematical analysis of the connectivity and security properties of sensor networks that make use of the random predistribution of keys. We also show how to set the parameters---pool and key ring size---in such a way that the network is not only connected ... Keywords: Wireless sensor network, connectivity, probabilistic key sharing, random graphs 20 January 2008 SODA '08: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 8 Downloads (6 Weeks): 1,   Downloads (12 Months): 3,   Downloads (Overall): 253 Full text available: PDF We consider the problem of minimizing average latency cost while obliviously routing traffic in a network with linear latency functions. This is roughly equivalent to minimizing the function Σ e (load( e )) 2 , where for a network link e , load( e ) denotes the amount of traffic ...