M. Trepanier,* Daimeng Zhang, Oleg Mukhanov, and Steven M. Anlage Department of Physics, CNAM, University of Maryland, College Park, Maryland 20742-4111, USA Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742-3285, USA Hypres, Inc., 175 Clearbrook Road, Elmsford, New York 10523, USA (Received 26 July 2013; revised manuscript received 22 Octob...

Gilad Ben-Shach,1 Arbel Haim,2 Ian Appelbaum,3 Yuval Oreg,2 Amir Yacoby,1 and Bertrand I. Halperin1 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 2Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel 3Center for Nanophysics and Advanced Materials, University of Maryland, College Park, Maryland 20742-4111, USA (Received 17...

Yunglung Chen, Yuping Wang, Kinshuk, Nian-Shing Chen Department of Information Management, National Sun Yat-sen University, No. 70, Lienhai Rd., Kaohsiung 80424, Taiwan School of Languages and Linguistics, Griffith University, Nathan, 4111, Australia School of Computing and Information System, Athabasca University, Athabasca, Canada [email protected], [email protected], kinshuk@athabas...

Theorem 8.2 [CR92] The threshold r2 exists and is r2 = 1. Proof: We proved one direction of Theorem 8.2 in the last lecture, by showing that Pr[φ is satisfiable]→ 1 for r ≤ (1− ). We now prove the other direction. Assume m = (1 + )n. Define t = n. (We’ll see the reason for this choice later.) The approach we’ll take is to define a collection of sets of clauses that are not satisfiable, and then...

We characterize the structure of maximum-size sum-free subsets of a random subset of an Abelian group G. In particular, we determine the threshold above which, with high probability as |G| → ∞, each such subset is contained in some maximum-size sum-free subset of G, whenever q divides |G| for some (fixed) prime q with q ≡ 2 (mod 3). Moreover, in the special case G = Z2n, we determine the sharp ...

This paper presents a deterministic and efficient algorithm for online facility location. The algorithm is based on a simple hierarchical partitioning and is extremely simple to implement. It also applies to a variety of models, i.e., models where the facilities can be placed anywhere in the region, or only at customer sites, or only at fixed locations. The paper shows that the algorithm is O(l...

We show that several versions of Floyd and Rivest’s algorithm Select for finding the kth smallest of n elements require at most n+min{k, n− k}+ o(n) comparisons on average and with high probability. This rectifies the analysis of Floyd and Rivest, and extends it to the case of nondistinct elements. Our computational results confirm that Select may be the best algorithm in practice.

We prove that, with high probability, the space complexity of refuting a random unsatisfiable boolean formula in -CNF on variables and clauses is .