We show the following results for rounds/time tradeoffs in the two person pebble game. 1. For every R and n (R =O (n /logn )), there is a bounded degree graph of n vertices for which the Pebbler can win in R rounds only in time Ω(n /logR ). 2. There is a graph that exhibits almost tight round/time tradeoffs for all rounds. 3. There is no graph with tight round/time tradeoffs for all rounds. As ...

In nonrelativistic quantum theories with short-range Hamiltonians, a velocity v can be chosen such that the influence of any local perturbation is approximately confined to within a distance r until a time t∼r/v, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law (1/r^{α}) interactions, when α exceeds the dimension D, an analogous b...

We study a problem motivated by rectilinear schematization of geographic maps. Given a biconnected plane graph G and an integer k ≥ 0, does G have a strictorthogonal drawing (i.e., an orthogonal drawing without edge bends) with at most k reflex angles per face? For k = 0, the problem is equivalent to realizing each face as a rectangle. We prove that the strict-orthogonal drawability problem for...

We study the problem of maintaining a (1+2)-factor approximation of the diameter of a stream of points under the sliding window model. In one dimension, we give a simple algorithm that only needs to store O( 1 2 logR) points at any time, where the parameter R denotes the “spread” of the point set. This bound is optimal and improves Feigenbaum, Kannan, and Zhang’s recent solution by two logarith...

The difference between the number of lattice points N(R) that lie in x2 + y2 :s R2 and the area of that circle, d(R) = N(R) 7rR2 , can be bounded by Id(R)1 :S KRIJ . Gauss showed that this holds for () = 1, but the least value for which it holds is an open problem in number theory. We have sought numerical evidence by tabulating N(R) up to R:::::: 55,000. From the convex hull bounding log Id(R)...

We present a simple algorithm to compute a convex decomposition of a non-convex, non-manifold polyhedron of arbitrary genus (handles). The algorithm takes a non-convex polyhedron with n edges and r notches (features causing non-convexity in the polyhedra) and produces a worst-case optimal O(r2 ) number of convex polyhedra Si, with U;S; = S, in O(nr2 ) time and O(nr) space. Recenlly, Chazelle an...

In this paper we derive quantitative uniqueness estimates at infinity for solutions to an elliptic equation with unbounded drift in the plane. More precisely, let u be a real solution to ∆u + W · ∇u = 0 in R2, where W is real vector and ‖W‖Lp(R2) ≤ K for 2 ≤ p <∞. Assume that ‖u‖L∞(R2) ≤ C0 and satisfies certain a priori assumption at 0. Then u satisfies the following asymptotic estimates at R ...

WASP-80 is one of only two systems known to contain a hot Jupiter which transits its M-dwarf host star. We present eight light curves of one transit event, obtained simultaneously using two defocussed telescopes. These data were taken through the Bessell I , Sloan griz and near-infrared JHK passbands. We use our data to search for opacity-induced changes in the planetary radius, but find that a...

We present a generic fetch-and-φ-based local-spin mutual exclusion algorithm, with O(1) time complexityunder the remote-memory-references time measure. This algorithm is “generic” in the sense that it can beimplemented using any fetch-and-φ primitive of rank 2N , where N is the number of processes. The rank ofa fetch-and-φ primitive is a notion introduced herein; informally, it expr...