Maximum algebraic connectivity augmentation is NP-hard
نویسنده
چکیده
The algebraic connectivity of a graph, which is the second-smallest eigenvalue of the Laplacian of the graph, is a measure of connectivity. We show that the problem of adding a specified number of edges to an input graph to maximize the algebraic connectivity of the augmented graph is NP-hard.
منابع مشابه
Complexity of Increasing the Secure Connectivity in Wireless Ad Hoc Networks
We consider the problem of maximizing the secure connectivity in wireless ad hoc networks, and analyze complexity of the postdeployment key establishment process constrained by physical layer properties such as connectivity, energy consumption and interference. Two approaches, based on graph augmentation problems with nonlinear edge costs, are formulated. The first one is based on establishing ...
متن کاملHard constraint satisfaction problems have hard gaps at location 1 1
An instance of the maximum constraint satisfaction problem (Max CSP) is a nite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satis ed constraints. Max CSP captures many well-known problems (such as Max k-SAT and Max Cut) and is consequently NP-hard. Thus, it is natural to study how restrictions on the allowed cons...
متن کاملApproximation Algorithms for Steiner Augmentations for Two-connectivity Approximation Algorithms for Steiner Augmentations for Two-connectivity
We consider the problem of increasing the connectivity of a given graph to two at optimal cost. Fredrickson and Ja'Ja' 6] showed that that this problem is NP-hard and provided approximation algorithms. Recently, Khuller and Thurimella 7] have extended these results and presented a more eecient version of the results in 6]. We consider an extension of this problem to a more general setting. In t...
متن کاملOn Finding the Maximum Number of DisjointCuts in
In the CUT PACKING problem, given an undirected connected graph G, it is required to nd the maximum number of pairwise edge disjoint cuts in G. It is an open question if CUT PACKING is NP-hard on general graphs. In this paper we prove that the problem is polynomially solvable on Seymour graphs which include both all bipar-tite and all series-parallel graphs. We also consider the weighted versio...
متن کاملAugmenting the Connectivity of Planar and Geometric Graphs
In this paper we study connectivity augmentation problems. Given a connected graph G with some desirable property, we want to make G 2-vertex connected (or 2-edge connected) by adding edges such that the resulting graph keeps the property. The aim is to add as few edges as possible. The property that we consider is planarity, both in an abstract graph-theoretic and in a geometric setting, where...
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:
- Oper. Res. Lett.
دوره 36 شماره
صفحات -
تاریخ انتشار 2008