We provide a quasilinear time algorithm for the p-center problem with an additive error less than or equal to 3 times the input graph’s hyperbolic constant. Specifically, for the graph G = (V,E) with n vertices, m edges and hyperbolic constant δ, we construct an algorithm for p-centers in time O(p(δ + 1)(n + m) log(n)) with radius not exceeding rp + δ when p ≤ 2 and rp + 3δ when p ≥ 3, where rp...

A basic question in computational geometry is how to find the relationship between a set of points and a line in a real plane. In this paper, we present multidimensional data structures for N points that allow answering the following queries for any given input line: (1) estimate in O(log N) time the number of points below the line; (2) return in O(log N + k) time the k ≤ N points that are belo...

We present new improved algorithms for the sorting problem. The algorithms are not only eecient but also clear and simple. First, we introduce Forward Radix Sort which combines the advantages of traditional left-to-right and right-to-left radix sort in a simple manner. We argue that this algorithm will work very well in practice. Adding a preprocessing step, we obtain an algorithm with attracti...

We propose a fast variant of the Gaussian algorithm for the reduction of two– dimensional lattices for the l1−, l2− and l∞−norm. The algorithm runs in at most O(nM(B) log B) bit operations for the l∞−norm and in O(n log n M(B) log B) bit operations for the l1− and l2−norm on input vectors a, b ∈ ZZ with norm at most 2 where M(B) is a time bound for B-bit integer multiplication. This generalizes...

We consider the problem of 0nding in an undirected graph a minimum cut that separates exactly a given number k of vertices. For general k (i.e. k is part of the input and may depend on n) this problem is NP-hard. We present for this problem a randomized approximation algorithm, which is useful when k is relatively small. In particular, for k = O(log n) we obtain a polynomial time approximation ...

We revisit the classical algorithms for searching over sorted sets and introduce an algorithm refinement, called adaptive search, that combines the good features of Interpolation search and those of Binary search. W.r.t. Insertion sort, only a constant number of extra comparisons is introduced. Yet, under several relevant input data distributions our algorithm shows average case cost comparable...

of O(n log n) algorithm Step1(initial procedure) Initialize a binary tree BT . Step2(update procedure) If possible, update BT . Else, exit the algorithm. Step3(test procedure) Test candidate pairs of jobs. Go to Step2. Let Lpair(v) be a set of values fpair(i, j) of v. The initial procedure is below. Initial procedure Step1 Put indices to jobs so that d1 < d2 < · · · < dn. Step2 Construct a bina...

We revisit the classical algorithms for searching over sorted sets to introduce an algorithm refinement, called Adaptive Search, that combines the good features of Interpolation search and those of Binary search. W.r.t. Interpolation search, only a constant number of extra comparisons is introduced. Yet, under diverse input data distributions our algorithm shows costs comparable to that of Inte...

We study the problem of using sorters of k vabxes to form large sorting and merging networks. For n an integral power of k, we show how to merge k sorted vectors of length n/k each using 4 log, n 3 layers of k-sorters and 4 log* n 5 layers of k=ittiqut binary mergers. As a result, we show how to sort R v&es using 2 iag$ n -log, n layers of k-sorters and 2 logf n 3 fog& n * I fayers of k-input l...

Network security has become more important role today to personal users and organizations. Denial-ofService (DoS) and Distributed Denial-of-Service (DDoS) attacks are serious problem in network. The major challenges in design of an efficient algorithm in data stream are one-pass over the input, poly-log space, poly-log update time and poly-log reporting time. In this paper, we use strongly expl...