Let C ⊂ Pn be a rational normal curve and let `O : Pn+1 99K Pn be any tangential projection form a point O ∈ TAC where A ∈ C. In this paper we relate the minimum number r of addenda that are needed to write a binary form p of degree (n + 1) and defined over an algebraically closed field of characteristic zero as linear combination of (n+1)-th powers of linear binary forms L1, . . . , Lr, with t...

This paper presents new heuristic algorithms using the guided A* search method : Guided Minimum Detour (GMD) algorithm and Line-by-Line Guided Minimum Detour (LGMD) algorithm for finding optimal rectilinear (L,) shortest paths in the presence of rectilinear obstacles. The GMD algorithm runs O(nhr(1ogN) + tN) in time and takes O(N) in space, where N is the number of extended line segments includ...

We propose a new method for finding the minimum ratio-cut of a graph. Ratio-cut is NP-hard problem for which the best previously known algorithm gi ves an O(log n)-factor approximation by solving its dually related maximum concurrent flow problem. We formulate the minimum ratio-cut as a certain nondifferentiable optimization problem, and sho w that the global minimum of the optimization problem...

Let G be a connected undirected and weighted graph with n vertices and m edges A most vital edge of G with respect to minimum spanning tree is an edge whose removal from G will cause the greatest weight increase in the minimum spanning tree of the remaining graph This paper presents fast parallel algorithms that compute the most vital edge of G in O logn time using O m log log logn logn n CRCW ...

In this work, the fast remediation of tert-butyl mercaptan from the polluted soil via a bimetallic Fenton treatment that included Fe2+/Fe3+/Fe0/Cu2+ in the presence of gasoline was studied. The analysis of variance and the Pareto analysis resulting from the central composite design (CCD) showed that the H2O2, CuSO4<...

In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse c...

Given a static array of n totally ordered object, the range minimum query problem is to build an additional data structure that allows to answer subsequent on-line queries of the form “what is the position of a minimum element in the sub-array ranging from i to j?” efficiently. We focus on two settings, where (1) the input array is available at query time, and (2) the input array is only availa...

A bipartite graph G = (X,Y ;E) is convex if there exists a linear enumeration L of the vertices of X such that the neighbours of each vertex of Y are consecutive in L. We show that the problems of finding a minimum dominating set and a minimum independent dominating set in an n-vertex convex bipartite graph are solvable in time O(n2). This improves previous O(n3) algorithms for these problems. ...

Random sampling i s a powerful way t o gather informat ion about a group by considering only a small part of it. W e give a paradigm f o r applying this technique to optimization problems, and demonstrate its effectiveness o n matroids. Matroids abstractly model many optimization problems that can be solved by greedy methods, such as the minimum spanning tree ( M S T ) problem. Our results have...

We present O(log logn)-round algorithms in the Massively Parallel Computation (MPC) model, with Õ(n) memory per machine, that compute a maximal independent set, a 1 + ε approximation of maximum matching, and a 2+ ε approximation of minimum vertex cover, for any n-vertex graph and any constant ε > 0. These improve the state of the art as follows: • Our MIS algorithm leads to a simple O(log log∆)...