Directed Steiner Problems with Connectivity Constraints
نویسنده
چکیده
We present a generalization of the Steiner problem in a directed graph. Given nonnegative weights on the arcs, the problem is to find a minimum weight subset F of the arc set such that the subgraph induced by F contains a given number of arc-disjoint directed paths from a certain root node to each given terminal node. Some applications of the problem are discussed and properties of associated polyhedra are studied. Results from a cutting plane algorithm are reported. Kej~words. Directed Steiner problem, connectivity constraints, facets, cutting plane algorithm.
منابع مشابه
On Approximate Min-Max Theorems for Graph Connectivity Problems by Lap
On Approximate Min-Max Theorems for Graph Connectivity Problems Lap Chi Lau Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2006 Given an undirected graph G and a subset of vertices S ⊆ V (G), we call the vertices in S the terminal vertices and the vertices in V (G) − S the Steiner vertices. In this thesis, we study two problems whose goals are to achieve high...
متن کاملApproximating minimum cost connectivity problems
We survey approximation algorithms and hardness results for versions of the Generalized Steiner Network (GSN) problem in which we seek to find a low cost subgraph (where the cost of a subgraph is the sum of the costs of its edges) that satisfies prescribed connectivity requirements. These problems include the following well known problems: min-cost k-flow, min-cost spanning tree, traveling sale...
متن کاملEdge-connectivity of undirected and directed hypergraphs
The objective of the thesis is to discuss edge-connectivity and related connectivity conceptsin the context of undirected and directed hypergraphs. In particular, we focus on k-edge-connectivity and (k, l)-partition-connectivity of hypergraphs, and (k, l)-edge-connectivityof directed hypergraphs. A strong emphasis is placed on the role of submodularity in thestructural aspects o...
متن کاملSurvivable Network Design with Degree or Order
We present algorithmic and hardness results for network design problems with degree or order constraints. The first problem we consider is the Survivable Network Design problem with degree constraints on vertices. The objective is to find a minimum cost subgraph which satisfies connectivity requirements between vertices and also degree upper bounds Bv on the vertices. This includes the well-stu...
متن کاملStrong formulations for network design problems with connectivity requirements
The network design problem with connectivity requirements (NDC) models a wide variety of celebrated combinatorial optimization problems including the minimum spanning tree, Steiner tree, and survivable network design problems. We develop strong formulations for two versions of the edge-connectivity NDC problem: unitary problems requiring connected network designs, and nonunitary problems permit...
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:
- Discrete Applied Mathematics
دوره 47 شماره
صفحات -
تاریخ انتشار 1993