A new dynamic Interpolation Search (IS) data structure is presented that achieves O(log log n) search time with high probability on unknown continuous or even discrete input distributions with measurable probability of key collisions, including power law and Binomial distributions. No such previous result holds for IS when the probability of key collisions is measurable. Moreover, our data stru...

We present a distributed randomized algorithm finding Minimum Spanning Tree (MST) of a given graph in O(1) rounds, with high probability, in the congested clique model. The input graph in the congested clique model is a graph of n nodes, where each node initially knows only its incident edges. The communication graph is a clique with limited edge bandwidth: each two nodes (not necessarily neigh...

Given an array X of n elements from a restricted domain of integers [1, n]. The integer sorting problem is the rearrangement of n integers in ascending order. We study the first optimal deterministic sublogarithmic algorithm for integer sorting on CRCW PRAM. We give two comments on the algorithm. The first comment is the algorithm not runs in sublogarithmic time for any distribution of input da...

We present an algorithm that on input a graph G with n vertices and m+ n− 1 edges and a value k, produces an incremental sparsifier Ĝ with n − 1 +m/k edges, such that the condition number of G with Ĝ is bounded above by Õ(k log n), with probability 1− p. The algorithm runs in time Õ((m log n+ n log n) log(1/p)). As a result, we obtain an algorithm that on input an n × n symmetric diagonally dom...

The combinatorial explosion of motif patterns occurring in 1D and 2D arrays leads to the consideration of special classes of motifs growing linearly with the size of the input array. Such motifs, called irredundant motifs, are able to succinctly represent all of the other motifs occurring in the same array within reasonable time and space bounds. In previous work irredundant motifs were extract...

Pattern of data access is independent of data values. • Server holds n items, encrypted. • Client has W = O(log n) working storage. • No Random-Oracles. • Best DO RAM simulation: O(log3 n) overhead [2]. • Using compressed-scanning: only O(log n) overhead. Compressed-Scanning In t rounds: • Read batch of Bin < W items from input. Each item of input read exactly once. Permutation π hides access p...

In this paper we focus on the problem of designing very fast parallel algorithms for the planar convex hull problem that achieve the optimal O(n log H) work-bound for input size n and output size H. Our algorithms are designed for the arbitrary CRCW PRAM model. We first describe a very simple ©(log n log H) time optimal deterministic algorithm for the planar hulls which is an improvement over t...

The importance of the sensitivity of an algorithm to the output size of a problem is well known especially if the upper bound on the output size is known to be not too large. In this paper we focus on the problem of designing very fast parallel algorithms for constructing the upper envelope of straight-line segments that achieve the O(n logH) work-bound for input size n and output size H. When ...

The Lempel-Ziv parsing of a string (LZ77 for short) is one of the most important and widely-used algorithmic tools in data compression and string processing. We show that the LempelZiv parsing of a string of length n on an alphabet of size σ can be computed in O(n log log σ) time (O(n) time if we allow randomization) using O(n log σ) bits of working space; that is, using space proportional to t...