Sharif Digital Repository

Given a simple polygon P with n vertices, the visibility polygon (V P) of a point q (V P(q)), or a segment (formula present) (V P(pq)) inside P can be computed in linear time. We propose a linear time algorithm to extend V P of a viewer (point or segment), by converting some edges of P into mirrors, such that a given non-visible segment (formula present) can also be seen from the viewer. Various definitions for the visibility of a segment, such as weak, strong, or complete visibility are considered. Our algorithm finds every edge such that, when converted to a mirror, makes (formula present) visible to our viewer. We find out exactly which interval of (formula present) becomes visible, by... 

Given a simple polygon P with n vertices, the visibility polygon (VP) of a point q, or a segment pq‾ inside P can be computed in linear time. We propose a linear time algorithm to extend the VP of a viewer (point or segment), by converting some edges of P into mirrors, such that a given non-visible segment uw‾ can also be seen from the viewer. Various definitions for the visibility of a segment, such as weak, strong, or complete visibility are considered. Our algorithm finds every edge that, when converted to a mirror, makes uw‾ visible to our viewer. We find out exactly which interval of uw‾ becomes visible, by every edge middling as a mirror, all in linear time. In other words, in this... 

The visibility graph of a polygon corresponds to its internal diagonals and boundary edges. For each vertex on the boundary of the polygon, we have a vertex in this graph and if two vertices of the polygon see each other there is an edge between their corresponding vertices in the graph. Two vertices of a polygon see each other if and only if their connecting line segment completely lies inside the polygon. Recognizing visibility graphs is the problem of deciding whether there is a simple polygon whose visibility graph is isomorphic to a given graph. Another important problem is to reconstruct such a polygon if there is any. These problems are well known and well-studied, but yet open... 

Hierarchical reinforcement learning (HRL) has had a vast range of applications in recent years. Preparing mechanisms for autonomous acquisition of skills has been a main topic of research in this area. While different methods have been proposed to achieve this goal, few methods have been shown to be successful both in performance and also efficiency in terms of time complexity of the algorithm. In this paper, a linear time algorithm is proposed to find subgoal states of the environment in early episodes of learning. Having subgoals available in early phases of a learning task, results in building skills that dramatically increase the convergence rate of the learning process. © 2009 Springer... 

The anti-Ramsey numbers are a fundamental notion in graph theory, introduced in 1978, by Erdös, Simonovits and Sós. For given graphs G and H the anti-Ramsey number ar(G, H) is defined to be the maximum number k such that there exists an assignment of k colors to the edges of G in which every copy of H in G has at least two edges with the same color. Usually, combinatorists study extremal values of anti-Ramsey numbers for various classes of graphs. There are works on the computational complexity of the problem when H is a star. Along this line of research, we study the complexity of computing the anti-Ramsey number ar(G, Pk), where Pk is a path of length k. First, we observe that when k is...