A Polynomial-Time Algorithm for Outerplanar Diameter Improvement
نویسندگان
چکیده
The Outerplanar Diameter Improvement problem asks, given a graph G and an integer D, whether it is possible to add edges to G in a way that the resulting graph is outerplanar and has diameter at most D. We provide a dynamic programming algorithm that solves this problem in polynomial time. Outerplanar Diameter Improvement demonstrates several structural analogues to the celebrated and challenging Planar Diameter Improvement problem, where the resulting graph should, instead, be planar. The complexity status of this latter problem is open.
منابع مشابه
A Polynomial Time Algorithm for Obtaining a Minimum Vertex Ranking Spanning Tree in Outerplanar Graphs
The minimum vertex ranking spanning tree problem is to find a spanning tree of G whose vertex ranking is minimum. This problem is NP-hard and no polynomial time algorithm for solving it is known for non-trivial classes of graphs other than the class of interval graphs. This paper proposes a polynomial time algorithm for solving the minimum vertex ranking spanning tree problem on outerplanar gra...
متن کاملGenerating Outerplanar Graphs Uniformly at Random
We show how to generate labeled and unlabeled outerplanar graphs with n vertices uniformly at random in polynomial time in n. To generate labeled outerplanar graphs, we present a counting technique using the decomposition of a graph according to its block structure, and compute the exact number of labeled outerplanar graphs. This allows us to make the correct probabilistic choices in a recursiv...
متن کاملAn Expressive Outerplanar Graph Pattern Class and its Efficient Pattern Matching Algorithm
An outerplanar graph is a planar graph which can be embedded in the plane in such a way that all of vertices lie on the outer boundary. Many chemical compounds are known to be expressed by outerplanar graphs. An externally extensible outerplanar graph pattern (eeo-graph pattern for short) represents a graph pattern common to a finite set of outerplanar graphs like a dataset of chemical compound...
متن کاملA Polynomial-Time Algorithm for Computing the Maximum Common Connected Edge Subgraph of Outerplanar Graphs of Bounded Degree
The maximum common connected edge subgraph problem is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs, where it has applications in pattern recognition and chemistry. This paper presents a dynamic programming algorithm for the problem when the two input graphs are outerplanar graphs of a bounded vertex degree, where it ...
متن کاملA Polynomial-time Metric for Outerplanar Graphs
Graphs are mathematical structures that are capable of representing relational data. In the chemoinformatics context, they have become very popular for the representation of molecules. However, a lot of operations on graphs are NP-complete, so no efficient algorithms that can handle these structures exist. In this paper we focus on outerplanar graphs, a subclass within general graphs. Most mole...
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