This paper first presents a unified approach to design efficient algorithms for the weighted domination problem and its three variants, i.e., the weighted independent, connected, and total domination problems, on interval graphs. Given an interval model with endpoints sorted, these algorithms run in time O(n) or O(n log log n) where n is the number of vertices. The results are then extended to solve the same problems on circular-arc graphs in O(n + m) time where m is the number of edges of the input graph.

Efficient Algorithms for the Domination Problems on Interval and Circular-Arc Graphs

In this paper, we present a self-stabilizing algorithm for finding cut-nodes and bridges in arbitrary rooted networks with a low memory requirement (O(log(n)) bits per processor where n is the number of processors). Our algorithm is silent and must be composed with a silent self-stabilizing algorithm computing a Depth-First Search (DFS) Spanning Tree of the network. So, in the paper, we will prove that the composition of our algorithm with any silent self-stabilizing DFS algorithm is self-stabilizing. Finally, we will show that our algorithm needs O(n2) moves to reach a terminal configuration once the DFS spanning tree is computed. Note that this time complexity is equivalent to the best proposed solutions.

A silent self-stabilizing algorithm for finding cut-nodes and bridges

In this paper, a self-stabilizing algorithm is presented for finding the articulation points of a connected undirected graph on a distributed or network model of computation after O(n2|E|) moves. The algorithm is resilient to transient faults and does not require initialization. A correctness proof of the algorithm is also presented. The paper concludes with remarks on issues such as the time complexity of the algorithm and open problems.

A self-stabilizing algorithm for finding articulation points

Based on the geometric representation, an efficient algorithm is designed to find all articulation points of a permutation graph. The proposed algorithm takes onlyO(n logn) time andO(n) space, wheren represents the number of vertices. The proposed sequential algorithm can easily be implemented in parallel which takesO(logn) time andO(n) processors on an EREW PRAM. These are the first known algorithms for the problem on this class of graph.

Efficient algorithms to compute all articulation points of a permutation graph

Parallel Algorithms on Interval Graphs.

Optimal parallel algorithms for finding cut vertices and bridges of interval graphs

Some topics in graph theory

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Sufficient conditions for edge-locally connected and $n$-connected graphs

The local connectivity, vk(G) , of a graph G is the minimum of the connectivities of neighbourhoods of the vertices of G . G is minimally locally w-connected if vk(G) = n and for every edge x of G , vk(G-x) = n - 1 . A necessary and sufficient condition for a locally connected graph to be minimally locally 1-connected is given, and it is shown that for

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K. H. Kulkarni

Papers

Optimal parallel algorithms for finding cut vertices and bridges of interval graphs

Some topics in graph theory

Sufficient conditions for edge-locally connected and $n$-connected graphs

Minimally locally 1-connected graphs