Paths with Minimum Range and Ratio of Arc Lengths
نویسندگان
چکیده
Two new path problems in graphs are studied: MINRANGE, i.e., find a path from a vertex s to a vertex 1 with the smallest possible range of arc lengths. and MINRATIO, i.e., find such a path for which the ratio of the largest to the smallest arc length is minimum. Several bicriterion extensions of these problems are also considered. Ke_vwords: Bicriterion paths; Range; Ratio
منابع مشابه
Differential Geometric Path Planning of Multiple UAVs
Safe and simultaneous arrival of constant speed, constant altitude unmanned air vehicles (UAVs) on target is solved by design of paths of equal lengths. The starting point for our solution is the well-known Dubins path, which is composed of circular arc and line segments, thus requiring only one simple maneuver—constant rate turn. An explicit bound can be imposed on the rate during the design a...
متن کاملInapproximability results for the inverse shortest paths problem with integer lengths and unique shortest paths
We study the complexity of two Inverse Shortest Paths (ISP) problems with integer arc lengths and the requirement for uniquely determined shortest paths. Given a collection of paths in a directed graph, the task is to find positive integer arc lengths such that the given paths are uniquely determined shortest paths between their respective terminals. The first problem seeks for arc lengths that...
متن کاملConversion of Network Problem with Transfer Nodes, and Condition of Supplying the Demand of any Sink from the Particular Source to the Transportation Problem
In this article we present an algorithm for converting a network problem with several sources and several sinks including several transfer nodes and condition of supplying the demand of any sink from a particular source to the transportation problem. Towards this end, and considering the very special structure of transportation algorithm, after implementing the shortest path algorithm or ...
متن کاملFinding minimum cost to time ratio cycles with small integral transit times
Let D = (V, E) be a digraph with n vertices and m arcs. For each e E E there is an associated cost ce and a transit time te; Ce can be arbitrary, but we require t to be a non-negative integer. The cost to time ratio of a cycle C is X(C) = 3 ec ceCeec t. Let E' c E denote the set of arcs e with te > 0, let T = max{tv: (u, v) E} for each vertex u, and let T = uev T. We give a new algorithm for fi...
متن کاملComplete classification of tournaments having a disjoint union of directed paths as a minimum feedback arc set
A feedback arc set of a digraph is a set of arcs whose reversal makes the resulting digraph acyclic. Given a tournament with a disjoint union of directed paths as a feedback arc set, we present necessary and sufficient conditions for this feedback arc set to have minimum size. We will present a construction for tournaments where the difference between the size of a minimum feedback arc set and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 78 شماره
صفحات -
تاریخ انتشار 1997