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Range Minima Queries with Respect to a Random Permutation, and Approximate Range Counting

of Computer Science, Universidad Nacional de Colombia , Medellín , Colombia 1 H. Kaplan, 2 The work by Haim Kaplan was partially supported by Grant 2006/204 from the U.S.-Israel Binational Science

On Lines and Joints

U.S.-Israeli Binational Science Foundation. Work by Haim Kaplan was also supported by Grant 975/06 from the Israel Science Fund, and by Grant 2006/204 from the U.S.-Israel Binational Science Foundation

Stabbing Pairwise Intersecting Disks by Five Points

Wolfgang Mulzer 2 Institut für Informatik, Freie Universität Berlin , 14195 Berlin, Germany 3 Haim Kaplan School of Computer Science, Tel Aviv University , Tel Aviv

Output Sensitive Algorithms for Approximate Incidences and Their Applications

An epsilon-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most epsilon from each other. Given a set of points and a set of objects, computing the approximate incidences between them is a major step in many database and web-based applications in computer vision and graphics...

Finding Axis-Parallel Rectangles of Fixed Perimeter or Area Containing the Largest Number of Points

algorithms for these problems, significantly improving the current state of the art. 1998 ACM Subject Classification F.2.2 Geometrical problems and computations, E.1 Data structures ? Work by Haim Kaplan has

Clustering in Hypergraphs to Minimize Average Edge Service Time

invariants that one can utilize. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems ? Work by Haim Kaplan has been supported by Grant 1161/2011 from the German-Israeli Science

Min-Cost Bipartite Perfect Matching with Delays

. In Proceedings of the 2016 ACM Conference on Economics and Computation , page 765 , 2016 . doi: 10 .1145/2940716.2940758. Yossi Azar , Ashish Chiplunkar, and Haim Kaplan . Polylogarithmic bounds on the

Spanners and Reachability Oracles for Directed Transmission Graphs

Let P be a set of n points in d dimensions, each with an associated radius r_p > 0. The transmission graph G for P has vertex set P and an edge from p to q if and only if q lies in the ball with radius r_p around p. Let t > 1. A t-spanner H for G is a sparse subgraph of G such that for any two vertices p, q connected by a path of length l in G, there is a p-q-path of length at...

Minimum Cost Flows in Graphs with Unit Capacities

We consider the minimum cost flow problem on graphs with unit capacities and its special cases. In previous studies, special purpose algorithms exploiting the fact that capacities are one have been developed. In contrast, for maximum flow with unit capacities, the best bounds are proven for slight modifications of classical blocking flow and push-relabel algorithms. In this paper...

Minimum s-t cut in undirected planar graphs when the source and the sink are close

Consider the minimum s-t cut problem in an embedded undirected planar graph. Let p be the minimum number of faces that a curve from s to $t$ passes through. If p=1, that is, the vertices s and t are on the boundary of the same face, then the minimum cut can be found in O(n)time. For general planar graphs this cut can be found in O(n log n) time. We unify these results and give an...

Selection from Heaps, Row-Sorted Matrices, and X+Y Using Soft Heaps

STOC , pages 554 - 563 , 2018 . doi: 10 .1145/3188745.3188770. Haim Kaplan , Robert Endre Tarjan, and Uri Zwick . Soft Heaps Simplified . SIAM Journal on Computing , 42 ( 4 ): 1660 - 1673 , 2013 . doi