Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree
نویسندگان
چکیده
In the Steiner tree problem, we are given as input a connected n-vertex graph with edge weights in {1, 2, . . . ,W}, and a subset of k terminal vertices. Our task is to compute a minimum-weight tree that contains all the terminals. We give an algorithm for this problem with running time O(7.97 ·n · logW ) using O(n · lognW · log k) space. This is the first single-exponential time, polynomial-space FPT algorithm for the weighted Steiner Tree problem.
منابع مشابه
Subexponential-Time Parameterized Algorithm for Steiner Tree on Planar Graphs
The well-known bidimensionality theory provides a method for designing fast, subexponentialtime parameterized algorithms for a vast number of NP-hard problems on sparse graph classes such as planar graphs, bounded genus graphs, or, more generally, graphs with a fixed excluded minor. However, in order to apply the bidimensionality framework the considered problem needs to fulfill a special densi...
متن کاملAn FPT algorithm in polynomial space for the Directed Steiner Tree problem with Limited number of Diffusing nodes
Given a directed graph with n nodes, a root r, a setX of k nodes called terminals and non-negative weights ω over the arcs, the Directed Steiner Tree problem (DST) asks for a directed tree T ∗ of minimum cost ω(T ∗) rooted at r and spanning X. If this problem has several applications in multicast routing in packet switching networks, the modeling is no longer adapted in networks based upon the ...
متن کاملFaster Steiner Tree Computation in Polynomial-Space
Given an n-node graph and a subset of k terminal nodes, the NP -hard Steiner tree problem is to compute a minimum-size tree which spans the terminals. All the known algorithms for this problem which improve on trivial O(1.62)-time enumeration are based on dynamic programming, and require exponential space. Motivated by the fact that exponential-space algorithms are typically impractical, in thi...
متن کاملOn subexponential parameterized algorithms for Steiner Tree and Directed Subset TSP on planar graphs
There are numerous examples of the so-called “square root phenomenon” in the field of parameterized algorithms: many of the most fundamental graph problems, parameterized by some natural parameter k, become significantly simpler when restricted to planar graphs and in particular the best possible running time is exponential in O( √ k) instead of O(k) (modulo standard complexity assumptions). We...
متن کاملSubexponential Parameterized Algorithms for Graphs of Polynomial Growth
We show that for a number of parameterized problems for which only 2O(k)nO(1) time algorithms are known on general graphs, subexponential parameterized algorithms with running time 2O(k 1− 1 1+δ log2 k)nO(1) are possible for graphs of polynomial growth with growth rate (degree) δ, that is, if we assume that every ball of radius r contains only O(r) vertices. The algorithms use the technique of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015