arXiv subjects
Publications and source records attributed to Nasrollah Moghaddam Charkari.
The purpose of this note is to give a simple proof for a necessary and sufficient condition for visibility paths in simple polygons. A visibility path is a curve such that every point inside a simple polygon is visible from at least one point on the path. This result is essential for finding the shortest watchman route inside a simple polygon specially when the route is restricted to curved paths.
We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning $P$ into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points $s$, $t$ and a query point $q$. Then, the proposed solution is extended to a general case for three arbitrary query points $s$, $t$ and $q$. In the former, we propose an algorithm with $O(n)$ preprocessing time. Extending this approach for the latter case, we develop an algorithm with $O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between $s$, $t$ as well as the path are provided in time $O(\log n)$ and $O(m+\log n)$, respectively, for the above two cases, where $m$ is the number of links.
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 shortest path map (SPM). In this paper, we present an optimal algorithm with $O(n)$ time bound, which is the same as the time complexity of the standard minimum link paths problem.
We investigate a practical variant of the well-known polygonal visibility path (watchman) problem. For a polygon $P$, a minimum link visibility path is a polygonal visibility path in $P$ that has the minimum number of links. The problem of finding a minimum link visibility path is NP-hard for simple polygons. If the link-length (number of links) of a minimum link visibility path (tour) is $Opt$ for a simple polygon $P$ with $n$ vertices, we provide an algorithm with $O(kn^2)$ runtime that produces polygonal visibility paths (or tours) of link-length at most $(γ+a_l/(k-1))Opt$ (or $(γ+a_l/k)Opt$), where $k$ is a parameter dependent on $P$, $a_l$ is an output sensitive parameter and $γ$ is the approximation factor of an $O(k^3)$ time approximation algorithm for the graphic traveling salesman problem (path or tour version).
Task scheduling problem in heterogeneous systems is the process of allocating tasks of an application to heterogeneous processors interconnected by high-speed networks, so that minimizing the finishing time of application as much as possible. Tasks are processing units of application and have precedenceconstrained, communication and also, are presented by Directed Acyclic Graphs (DAGs). Evolutionary algorithms are well suited for solving task scheduling problem in heterogeneous environment. In this paper, we propose a hybrid heuristic-based Artificial Immune System (AIS) algorithm for solving the scheduling problem. In this regard, AIS with some heuristics and Single Neighbourhood Search (SNS) technique are hybridized. Clonning and immune-remove operators of AIS provide diversity, while heuristics and SNS provide convergence of algorithm into good solutions, that is balancing between exploration and exploitation. We have compared our method with some state-of-the art algorithms. The results of the experiments show the validity and efficiency of our method.