1.757 and 1.267 - Approximation Algorithms for the Network and Rectilinear Steiner Tree Problems
نویسندگان
چکیده
The Steiner tree problem requires to nd a shortest tree connecting a given set of terminal points in a metric space. We suggest a better and fast heuristic for the Steiner problem in graphs and in rectilinear plane. This heuristic nds a Steiner tree at most 1.757 and 1.267 times longer than the optimal solution in graphs and rectilinear plane, respectively.
منابع مشابه
New Approximation Algorithms for the Steiner Tree Problems
The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using a novel technique of choosing Steiner points in dependence on the possible deviation from the optimal solutions. We achieve the best up to now approximation ratios of 1.644 in arbitrary metric and 1.267 in rec...
متن کاملProblem Heuristic Performance Ratio New PR Run - time
The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using a novel technique of choosing Steiner points in dependence on the possible deviation from the optimal solutions. We achieve the best up to now approximation ratios of 1.644 in arbitrary metric and 1.267 in rec...
متن کاملSubexponential Algorithms for Rectilinear Steiner Tree and Arborescence Problems
A rectilinear Steiner tree for a set T of points in the plane is a tree which connects T using horizontal and vertical lines, In the Rectilinear Steiner Tree problem, input is a set T of n points in the Euclidean plane (R) and the goal is to find an rectilinear Steiner tree for T of smallest possible total length. A rectilinear Steiner arborecence for a set T of points and root r ∈ T is a recti...
متن کاملFaster Approximation Algorithms for the Rectilinear Steiner Tree Problem
The classical Steiner tree problem requires a shortest tree spanning a given vertex subset within a graph G = (V, E). An important variant is the Steiner tree problem in rectilinear metric. Only recently two algorithms were found which achieve better approximations than the “traditional” one with a factor of 3/2. These algorithms with an approximation ratio of 11/8 are quite slow and run in tim...
متن کاملApproaching the 5/4-Approximation for Rectilinear Steiner Trees
The rectilinear Steiner tree problem requires a shortest tree spanning a given vertex subset in the plane with rectilinear distance. It was proved that the output length of Zelikovsky's 25] and Berman/Ramaiyer 3] heuristics is at most 1.375 and 97 72 1:347 of the optimal length, respectively. It was claimed that these bounds are not tight. Here we improve these bounds to 1.3125 and 61 48 1:271,...
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:
- Electronic Colloquium on Computational Complexity (ECCC)
دوره 2 شماره
صفحات -
تاریخ انتشار 1995