Approximating subset kk-connectivity problems

A subset $T \subseteq V$ of terminals is $k$-connected to a root $s$ in a directed/undirected graph $J$ if $J$ has $k$ internally-disjoint $vs$-paths for every $v \in T$; $T$ is $k$-connected in $J$ if $T$ is $k$-connected to every $s \in T$. We consider the {\sf Subset $k$-Connectivity Augmentation} problem: given a graph $G=(V,E)$ with edge/node-costs, node subset $T \subseteq V$, and a subgraph $J=(V,E_J)$ of $G$ such that $T$ is $k$-connected in $J$, find a minimum-cost augmenting edge-set $F \subseteq E \setminus E_J$ such that $T$ is $(k+1)$-connected in $J \cup F$. The problem admits trivial ratio $O(|T|^2)$. We consider the case $|T|>k$ and prove that for directed/undirected graphs and edge/node-costs, a $\rho$-approximation for {\sf Rooted Subset $k$-Connectivity Augmentation} implies the following ratios for {\sf Subset $k$-Connectivity Augmentation}: (i) $b(\rho+k) + {(\frac{3|T|}{|T|-k})}^2 H(\frac{3|T|}{|T|-k})$; (ii) $\rho \cdot O(\frac{|T|}{|T|-k} \log k)$, where b=1 for undirected graphs and b=2 for directed graphs, and $H(k)$ is the $k$th harmonic number. The best known values of $\rho$ on undirected graphs are $\min\{|T|,O(k)\}$ for edge-costs and $\min\{|T|,O(k \log |T|)\}$ for node-costs; for directed graphs $\rho=|T|$ for both versions. Our results imply that unless $k=|T|-o(|T|)$, {\sf Subset $k$-Connectivity Augmentation} admits the same ratios as the best known ones for the rooted version. This improves the ratios in \cite{N-focs,L}

Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements

The discrete acyclic convolution computes the 2n-1 sums sum_{i+j=k; (i,j) in [0,1,2,...,n-1]^2} (a_i b_j) in O(n log n) time. By using suitable offsets and setting some of the variables to zero, this method provides a tool to calculate all non-zero sums sum_{i+j=k; (i,j) in (P cap Z^2)} (a_i b_j) in a rectangle P with perimeter p in O(p log p) time. This paper extends this geometric interpretation in order to allow arbitrary convex polygons P with k vertices and perimeter p. Also, this extended algorithm only needs O(k + p(log p)^2 log k) time. Additionally, this paper presents fast algorithms for counting sub-cadences and cadences with 3 elements using this extended method

On the uniform generation of modular diagrams

In this paper we present an algorithm that generates $k$-noncrossing, $\sigma$-modular diagrams with uniform probability. A diagram is a labeled graph of degree $\le 1$ over $n$ vertices drawn in a horizontal line with arcs $(i,j)$ in the upper half-plane. A $k$-crossing in a diagram is a set of $k$ distinct arcs $(i_1, j_1), (i_2, j_2),\ldots,(i_k, j_k)$ with the property $i_1 < i_2 < \ldots < i_k < j_1 < j_2 < \ldots< j_k$. A diagram without any $k$-crossings is called a $k$-noncrossing diagram and a stack of length $\sigma$ is a maximal sequence $((i,j),(i+1,j-1),\dots,(i+(\sigma-1),j-(\sigma-1)))$. A diagram is $\sigma$-modular if any arc is contained in a stack of length at least $\sigma$. Our algorithm generates after $O(n^k)$ preprocessing time, $k$-noncrossing, $\sigma$-modular diagrams in $O(n)$ time and space complexity.Comment: 21 pages, 7 figure

Transverse-momentum dependent modification of dynamic texture in central Au+Au collisions at sqrt[sNN]=200GeV

Correlations in the hadron distributions produced in relativistic Au+Au collisions are studied in the discrete wavelet expansion method. The analysis is performed in the space of pseudorapidity (| eta | <= 1) and azimuth(full 2 pi ) in bins of transverse momentum (pt) from 0.14 <= pt <= 2.1GeV/c. In peripheral Au+Au collisions a correlation structure ascribed to minijet fragmentation is observed. It evolves with collision centrality and pt in a way not seen before, which suggests strong dissipation of minijet fragmentation in the longitudinally expanding medium.Alle Autoren: J. Adams, M. M. Aggarwal, Z. Ahammed, J. Amonett, B. D. Anderson, D. Arkhipkin, G. S. Averichev, S. K. Badyal, Y. Bai, J. Balewski, O. Barannikova, L. S. Barnby, J. Baudot, S. Bekele, V. V. Belaga, R. Bellwied, J. Berger, B. I. Bezverkhny, S. Bharadwaj, A. Bhasin, A. K. Bhati, V. S. Bhatia, H. Bichsel, A. Billmeier, L. C. Bland, C. O. Blyth, B. E. Bonner, M. Botje, A. Boucham, A. Brandin, A. Bravar, M. Bystersky, R. V. Cadman, X. Z. Cai, H. Caines, M. Calderón de la Barca Sánchez, J. Castillo, D. Cebra, Z. Chajecki, P. Chaloupka, S. Chattopdhyay, H. F. Chen, Y. Chen, J. Cheng, M. Cherney, A. Chikanian, W. Christie, J. P. Coffin, T. M. Cormier, J. G. Cramer, H. J. Crawford, D. Das, S. Das, M. M. de Moura, A. A. Derevschikov, L. Didenko, T. Dietel, S. M. Dogra, W. J. Dong, X. Dong, J. E. Draper, F. Du, A. K. Dubey, V. B. Dunin, J. C. Dunlop, M. R. Dutta Mazumdar, V. Eckardt, W. R. Edwards, L. G. Efimov, V. Emelianov, J. Engelage, G. Eppley, B. Erazmus, M. Estienne, P. Fachini, J. Faivre, R. Fatemi, J. Fedorisin, K. Filimonov, P. Filip, E. Finch, V. Fine, Y. Fisyak, K. Fomenko, J. Fu, C. A. Gagliardi, J. Gans, M. S. Ganti, L. Gaudichet, F. Geurts, V. Ghazikhanian, P. Ghosh, J. E. Gonzalez, O. Grachov, O. Grebenyuk, D. Grosnick, S. M. Guertin, Y. Guo, A. Gupta, T. D. Gutierrez, T. J. Hallman, A. Hamed, D. Hardtke, J. W. Harris, M. Heinz, T. W. Henry, S. Hepplemann, B. Hippolyte, A. Hirsch, E. Hjort, G. W. Hoffmann, H. Z. Huang, S. L. Huang, E. W. Hughes, T. J. Humanic, G. Igo, A. Ishihara, P. Jacobs, W. W. Jacobs, M. Janik, H. Jiang, P. G. Jones, E. G. Judd, S. Kabana, K. Kang, M. Kaplan, D. Keane, V. Yu. Khodyrev, J. Kiryluk, A. Kisiel, E. M. Kislov, J. Klay, S. R. Klein, A. Klyachko, D. D. Koetke, T. Kollegger, M. Kopytine, L. Kotchenda, M. Kramer, P. Kravtsov, V. I. Kravtsov, K. Krueger, C. Kuhn, A. I. Kulikov, A. Kumar, R. Kh. Kutuev, A. A. Kuznetsov, M. A. C. Lamont, J. M. Landgraf, S. Lange, F. Laue, J. Lauret, A. Lebedev, R. Lednicky, S. Lehocka, M. J. LeVine, C. Li, Q. Li, Y. Li, G. Lin, S. J. Lindenbaum, M. A. Lisa, F. Liu, L. Liu, Q. J. Liu, Z. Liu, T. Ljubicic, W. J. Llope, H. Long, R. S. Longacre, M. Lopez-Noriega, W. A. Love, Y. Lu, T. Ludlam, D. Lynn, G. L. Ma, J. G. Ma, Y. G. Ma, D. Magestro, S. Mahajan, D. P. Mahapatra, R. Majka, L. K. Mangotra, R. Manweiler, S. Margetis, C. Markert, L. Martin, J. N. Marx, H. S. Matis, Yu. A. Matulenko, C. J. McClain, T. S. McShane, F. Meissner, Yu. Melnick, A. Meschanin, M. L. Miller, N. G. Minaev, C. Mironov, A. Mischke, D. K. Mishra, J. Mitchell, B. Mohanty, L. Molnar, C. F. Moore, D. A. Morozov, M. G. Munhoz, B. K. Nandi, S. K. Nayak, T. K. Nayak, J. M. Nelson, P. K. Netrakanti, V. A. Nikitin, L. V. Nogach, S. B. Nurushev, G. Odyniec, A. Ogawa, V. Okorokov, M. Oldenburg, D. Olson, S. K. Pal, Y. Panebratsev, S. Y. Panitkin, A. I. Pavlinov, T. Pawlak, T. Peitzmann, V. Perevoztchikov, C. Perkins, 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. 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. Rogachevskiy, J. L. Romero, A. Rose, C. Roy, L. Ruan, R. Sahoo, I. Sakrejda, S. Salur, J. Sandweiss, I. Savin, P. S. Sazhin, J. Schambach, R. P. Scharenberg, N. Schmitz, K. Schweda, J. Seger, P. Seyboth, E. Shahaliev, M. Shao, W. Shao, M. Sharma, W. Q. Shen, K. E. Shestermanov, S. S. Shimanskiy, E. Sichtermann, F. Simon, R. N. Singaraju, G. Skoro, N. Smirnov, R. Snellings, G. Sood, P. Sorensen, J. Sowinski, J. Speltz, H. M. Spinka, B. Srivastava, A. Stadnik, T. D. S. Stanislaus, R. Stock, A. Stolpovsky, M. Strikhanov, B. Stringfellow, A. A. P. Suaide, E. Sugarbaker, C. Suire, M. Sumbera, B. Surrow, T. J. M. Symons, A. Szanto de Toledo, P. Szarwas, A. Tai, J. Takahashi, A. H. Tang, T. Tarnowsky, D. Thein, J. H. Thomas, S. Timoshenko, M. Tokarev, T. A. Trainor, S. Trentalange, R. E. Tribble, O. D. Tsai, J. Ulery, T. Ullrich, D. G. Underwood, A. Urkinbaev, G. Van Buren, M. van Leeuwen, A. M. Vander Molen, R. Varma, I. M. Vasilevski, A. N. Vasiliev, R. Vernet, S. E. Vigdor, Y. P. Viyogi, S. Vokal, S. A. Voloshin, M. Vznuzdaev, W. T. Waggoner, F. Wang, G. Wang, G. Wang, X. L. Wang, Y. Wang, Y. Wang, Z. M. Wang, H. Ward, J. W. Watson, J. C. Webb, R. Wells, G. D. Westfall, A. Wetzler, C. Whitten Jr., H. Wieman, S. W. Wissink, R. Witt, J. Wood, J. Wu, N. Xu, Z. Xu, Z. Z. Xu, E. Yamamoto, P. Yepes, V. I. Yurevich, Y. V. Zanevsky, H. Zhang, W. M. Zhang, Z. P. Zhang, P. A. Zolnierczuk, R. Zoulkarneev, Y. Zoulkarneeva, and A. N. Zubare