Approximation Algorithms for Connectivity

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Design Algorithms for Doppler MTI and Filters (Using Chebyshev Approximation)

Approximation Algorithms for the (S,T)-Connectivity Problems

We study a directed network design problem called the k-(S, T )-connectivity problem; we design and analyze approximation algorithms and give hardness results. For each positive integer k, the minimum cost k-vertex connected spanning subgraph problem is a special case of the k(S, T )-connectivity problem. We defer precise statements of the problem and of our results to the introduction. For k =...

A Survey on Stability Measure of Networks

In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower and upper bounds for tenacity.

Relay Placement Approximation Algorithms for k-Connectivity in Wireless Sensor Networks

Sensors typically use wireless transmitters to communicate with each other. However, sensors may be located in a way that they cannot even form a connected network (e.g, due to failures of some sensors, or loss of battery power). In this paper we consider the problem of adding the smallest number of additional (relay) nodes so that the induced communication graph is k-connected. The problem is ...

Approximation Algorithms for k-Connected Graph Factors

Finding low-cost spanning subgraphs with given degree and connectivity requirements is a fundamental problem in the area of network design. We consider the problem of finding d-regular spanning subgraphs (or d-factors) of minimum weight with connectivity requirements. For the case of k-edge-connectedness, we present approximation algorithms that achieve constant approximation ratios for all d ≥...