Algorithmic linear dimension reduction in the l_1 norm for sparse vectors

This paper develops a new method for recovering m-sparse signals that is simultaneously uniform and quick. We present a reconstruction algorithm whose run time, O(m log^2(m) log^2(d)), is sublinear in the length d of the signal. The reconstruction error is within a logarithmic factor (in m) of the optimal m-term approximation error in l_1. In particular, the algorithm recovers m-sparse signals perfectly and noisy signals are recovered with polylogarithmic distortion. Our algorithm makes O(m log^2 (d)) measurements, which is within a logarithmic factor of optimal. We also present a small-space implementation of the algorithm. These sketching techniques and the corresponding reconstruction algorithms provide an algorithmic dimension reduction in the l_1 norm. In particular, vectors of support m in dimension d can be linearly embedded into O(m log^2 d) dimensions with polylogarithmic distortion. We can reconstruct a vector from its low-dimensional sketch in time O(m log^2(m) log^2(d)). Furthermore, this reconstruction is stable and robust under small perturbations

A Fast Algorithm for Well-Spaced Points and Approximate Delaunay Graphs

We present a new algorithm that produces a well-spaced superset of points conforming to a given input set in any dimension with guaranteed optimal output size. We also provide an approximate Delaunay graph on the output points. Our algorithm runs in expected time $O(2^{O(d)}(n\log n + m))$, where $n$ is the input size, $m$ is the output point set size, and $d$ is the ambient dimension. The constants only depend on the desired element quality bounds. To gain this new efficiency, the algorithm approximately maintains the Voronoi diagram of the current set of points by storing a superset of the Delaunay neighbors of each point. By retaining quality of the Voronoi diagram and avoiding the storage of the full Voronoi diagram, a simple exponential dependence on $d$ is obtained in the running time. Thus, if one only wants the approximate neighbors structure of a refined Delaunay mesh conforming to a set of input points, the algorithm will return a size $2^{O(d)}m$ graph in $2^{O(d)}(n\log n + m)$ expected time. If $m$ is superlinear in $n$, then we can produce a hierarchically well-spaced superset of size $2^{O(d)}n$ in $2^{O(d)}n\log n$ expected time.Comment: Full versio

Succinct Dictionary Matching With No Slowdown

The problem of dictionary matching is a classical problem in string matching: given a set S of d strings of total length n characters over an (not necessarily constant) alphabet of size sigma, build a data structure so that we can match in a any text T all occurrences of strings belonging to S. The classical solution for this problem is the Aho-Corasick automaton which finds all occ occurrences in a text T in time O(|T| + occ) using a data structure that occupies O(m log m) bits of space where m <= n + 1 is the number of states in the automaton. In this paper we show that the Aho-Corasick automaton can be represented in just m(log sigma + O(1)) + O(d log(n/d)) bits of space while still maintaining the ability to answer to queries in O(|T| + occ) time. To the best of our knowledge, the currently fastest succinct data structure for the dictionary matching problem uses space O(n log sigma) while answering queries in O(|T|log log n + occ) time. In this paper we also show how the space occupancy can be reduced to m(H0 + O(1)) + O(d log(n/d)) where H0 is the empirical entropy of the characters appearing in the trie representation of the set S, provided that sigma < m^epsilon for any constant 0 < epsilon < 1. The query time remains unchanged.Comment: Corrected typos and other minor error

Pion-kaon correlations in central Au+Au collisions at sqrt[sNN]=130 GeV

Pion-kaon correlation functions are constructed from central Au+Au STAR data taken at sqrt[sNN]=130 GeV by the STAR detector at the Relativistic Heavy Ion Collider (RHIC). The results suggest that pions and kaons are not emitted at the same average space-time point. Space-momentum correlations, i.e., transverse flow, lead to a space-time emission asymmetry of pions and kaons that is consistent with the data. This result provides new independent evidence that the system created at RHIC undergoes a collective transverse expansion.alle Autoren: J. Adams, C. Adler, M. M. Aggarwal, Z. Ahammed, J. Amonett, B. D. Anderson, M. Anderson, D. Arkhipkin, G. S. Averichev, S. K. Badyal, J. Balewski, O. Barannikova, L. S. Barnby, J. Baudot, S. Bekele, V. V. Belaga, R. Bellwied, J. Berger, B. I. Bezverkhny, S. Bhardwaj, P. Bhaskar, A. K. Bhati, H. Bichsel, A. Billmeier, L. C. Bland, C. O. Blyth, B. E. Bonner, M. Botje, A. Boucham, A. Brandin, A. Bravar, R. V. Cadman, X. Z. Cai, H. Caines, M. Calderón de la Barca Sánchez, J. Carroll, J. Castillo, M. Castro, D. Cebra, P. Chaloupka, S. Chattopadhyay, H. F. Chen, Y. Chen, S. P. Chernenko, M. Cherney, A. Chikanian, B. Choi, W. Christie, J. P. Coffin, T. M. Cormier, J. G. Cramer, H. J. Crawford, D. Das, S. Das, A. A. Derevschikov, L. Didenko, T. Dietel, X. Dong, J. E. Draper, F. Du, A. K. Dubey, V. B. Dunin, J. C. Dunlop, M. R. Dutta Majumdar, V. Eckardt, L. G. Efimov, V. Emelianov, J. Engelage, G. Eppley, B. Erazmus, P. Fachini, V. Faine, J. Faivre, R. Fatemi, K. Filimonov, P. Filip, E. Finch, Y. Fisyak, D. Flierl, K. J. Foley, J. Fu, C. A. Gagliardi, M. S. Ganti, T. D. Gutierrez, N. Gagunashvili, J. Gans, L. Gaudichet, M. Germain, F. Geurts, V. Ghazikhanian, P. Ghosh, J. E. Gonzalez, O. Grachov, V. Grigoriev, S. Gronstal, D. Grosnick, M. Guedon, S. M. Guertin, A. Gupta, E. Gushin, T. J. Hallman, D. Hardtke, J. W. Harris, M. Heinz, T. W. Henry, S. Heppelmann, T. Herston, B. Hippolyte, A. Hirsch, E. Hjort, G. W. Hoffmann, M. Horsley, H. Z. Huang, S. L. Huang, T. J. Humanic, G. Igo, A. Ishihara, P. Jacobs, W. W. Jacobs, M. Janik, I. Johnson, P. G. Jones, E. G. Judd, S. Kabana, M. Kaneta, M. Kaplan, D. Keane, J. Kiryluk, A. Kisiel, J. Klay, S. R. Klein, A. Klyachko, D. D. Koetke, T. Kollegger, A. S. Konstantinov, M. Kopytine, L. Kotchenda, A. D. Kovalenko, M. Kramer, P. Kravtsov, K. Krueger, C. Kuhn, A. I. Kulikov, A. Kumar, G. J. Kunde, C. L. Kunz, R. Kh. Kutuev, A. A. Kuznetsov, M. A. C. Lamont, J. M. Landgraf, S. Lange, C. P. Lansdell, B. Lasiuk, F. Laue, J. Lauret, A. Lebedev, R. Lednický, V. M. Leontiev, M. J. LeVine, C. Li, Q. Li, S. J. Lindenbaum, M. A. Lisa, F. Liu, L. Liu, Z. Liu, Q. J. Liu, T. Ljubicic, W. J. Llope, H. Long, R. S. Longacre, M. Lopez-Noriega, W. A. Love, T. Ludlam, D. Lynn, J. Ma, Y. G. Ma, D. Magestro, S. Mahajan, L. K. Mangotra, D. P. Mahapatra, R. Majka, R. Manweiler, S. Margetis, C. Markert, L. Martin, J. Marx, H. S. Matis, Yu. A. Matulenko, T. S. McShane, F. Meissner, Yu. Melnick, A. Meschanin, M. Messer, M. L. Miller, Z. Milosevich, N. G. Minaev, C. Mironov, D. Mishra, J. Mitchell, B. Mohanty, L. Molnar, C. F. Moore, M. J. Mora-Corral, V. Morozov, M. M. de Moura, M. G. Munhoz, B. K. Nandi, S. K. Nayak, T. K. Nayak, J. M. Nelson, P. Nevski, V. A. Nikitin, L. V. Nogach, B. Norman, S. B. Nurushev, G. Odyniec, A. Ogawa, V. Okorokov, M. Oldenburg, D. Olson, G. Paic, S. U. Pandey, S. K. Pal, Y. Panebratsev, S. Y. Panitkin, A. I. Pavlinov, T. Pawlak, V. Perevoztchikov, W. Peryt, V. A. Petrov, S. C. Phatak, R. Picha, M. Planinic, J. Pluta, N. Porile, J. Porter, A. M. Poskanzer, M. Potekhin, E. Potrebenikova, B. V. K. S. Potukuchi, D. Prindle, C. Pruneau, J. Putschke, G. Rai, G. Rakness, R. Raniwala, S. Raniwala, O. Ravel, R. L. Ray, S. V. Razin, D. Reichhold, J. G. Reid, G. Renault, F. Retiere, A. Ridiger, H. G. Ritter, J. B. Roberts, O. V. Rogachevski, J. L. Romero, A. Rose, C. Roy, L. J. Ruan, V. Rykov, R. Sahoo, I. Sakrejda, S. Salur, J. Sandweiss, I. Savin, J. Schambach, R. P. Scharenberg, N. Schmitz, L. S. Schroeder, K. Schweda, J. Seger, D. Seliverstov, P. Seyboth, E. Shahaliev, M. Shao, M. Sharma, K. E. Shestermanov, S. S. Shimanskii, R. N. Singaraju, F. Simon, G. Skoro, N. Smirnov, R. Snellings, G. Sood, P. Sorensen, J. Sowinski, H. M. Spinka, B. Srivastava, S. Stanislaus, R. Stock, A. Stolpovsky, M. Strikhanov, B. Stringfellow, C. Struck, A. A. P. Suaide, E. Sugarbaker, C. Suire, M. Šumbera, B. Surrow, T. J. M. Symons, A. Szanto de Toledo, P. Szarwas, A. Tai, J. Takahashi, A. H. Tang, D. Thein, J. H. Thomas, V. Tikhomirov, M. Tokarev, M. B. Tonjes, T. A. Trainor, S. Trentalange, R. E. Tribble, M. D. Trivedi, V. Trofimov, O. Tsai, T. Ullrich, D. G. Underwood, G. Van Buren, A. M. VanderMolen, A. N. Vasiliev, M. Vasiliev, S. E. Vigdor, Y. P. Viyogi, S. A. Voloshin, W. Waggoner, F. Wang, G. Wang, X. L. Wang, Z. M. Wang, H. Ward, J. W. Watson, R. Wells, G. D. Westfall, C. Whitten, Jr., H. Wieman, R. Willson, S. W. Wissink, R. Witt, J. Wood, J. Wu, N. Xu, Z. Xu, Z. Z. Xu, A. E. Yakutin, E. Yamamoto, J. Yang, P. Yepes, V. I. Yurevich, Y. V. Zanevski, I. Zborovský, H. Zhang, H. Y. Zhang, W. M. Zhang, Z. P. Zhang, P. A. &#379;o&#322;nierczuk, R. Zoulkarneev, J. Zoulkarneeva, and A. N. Zubarev (STAR Collaboration

Optimal Query Complexity for Reconstructing Hypergraphs

In this paper we consider the problem of reconstructing a hidden weighted hypergraph of constant rank using additive queries. We prove the following: Let $G$ be a weighted hidden hypergraph of constant rank with n vertices and $m$ hyperedges. For any $m$ there exists a non-adaptive algorithm that finds the edges of the graph and their weights using $$O(\frac{m\log n}{\log m})$$ additive queries. This solves the open problem in [S. Choi, J. H. Kim. Optimal Query Complexity Bounds for Finding Graphs. {\em STOC}, 749--758,~2008]. When the weights of the hypergraph are integers that are less than $O(poly(n^d/m))$ where $d$ is the rank of the hypergraph (and therefore for unweighted hypergraphs) there exists a non-adaptive algorithm that finds the edges of the graph and their weights using $$O(\frac{m\log \frac{n^d}{m}}{\log m}).$$ additive queries. Using the information theoretic bound the above query complexities are tight