Let P be a path between two points s and t in a polygonal subdivision T with obstacles and weighted regions. Given a relative error tolerance ε ∈ (0, 1), we present the first algorithm to compute a path between s and t that can be deformed to P without passing over any obstacle and the path cost is within a factor 1 + ε of the optimum. The running time is O( 3 ε2 kn polylog(k, n, 1 ε )), where ...

The Web as a text corpus Pages close in word vector space tend to be related Cluster hypothesis (van Rijsbergen 1979) The WebCrawler (Pinkerton 1994) The whole first generation of search engines weapons mass destruction p 1 p 2 Enter the Web's link structure Broder & al. 2000 p(i) = α N + (1 − α) j:j→i p(j) Text Links Meaning Connection between semantic topology (topicality or relevance) and li...

This paper establishes the polynomial convergence of a new class of (feasible) primal-dual interior-point path following algorithms for semideenite programming (SDP) whose search directions are obtained by applying Newton method to the symmetric central path equation (P T XP) 1=2 (P ?1 SP ?T)(P T XP) 1=2 ? I = 0; where P is a nonsingular matrix. Speciically, we show that the short-step path fol...

ABSTRACT We propose a modified penalty embedding for solving complementarity problem (LCP). This embedding is a special one parametric optimization problem P(t), t∈[0,1]. Under the condition (A3) (a modified Enlarged Mangasarian Fromovitz Constrait Qualification), (A4) (P(t) is JongenJonker -Twilt regular) and two technical assumptions (A1) and (A2) there exists a path in the set of stationary ...

We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shor...

We show that a problem of deciding whether a formula for a multivariate polynomial of n variables over a finite field of characteristic 2 has degree n when reduced modulo a certain Boolean ideal belongs to ⊕ P. When the formula is allowed to have succinct representations as sums of monomials, the problem becomes ⊕ P-complete. key words: degree of multivariate polynomials, finite field of charac...

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