Interval Routing Schemes for Circular-Arc Graphs

Interval Routing Schemes for Circular-Arc Graphs

Interval routing is a space efficient method to realize a distributed routing function. In this paper we show that every circular-arc graph allows a shortest path strict 2-interval routing scheme, i.e., by introducing a global order on the vertices and assigning at most two (strict) intervals in this order to the ends of every edge allows to depict a routing function that implies exclusively sh...

Some Optimal Parallel Algorithms on Interval and Circular-arc Graphs

In this paper, we consider some shortest path related problems on interval and circular-arc graphs. For the all-pair shortest path query problem on interval and circular-arc graphs, instead of using the sophisticated technique, we propose simple parallel algorithms using only the parallel prefix and suffix computations and the Euler tour technique. Our preprocessing algorithms run in O(log n) t...

Paired domination on interval and circular-arc graphs

We study the paired-domination problem on interval graphs and circular-arc graphs. Given an interval model with endpoints sorted, we give an O(m + n) time algorithm to solve the paired-domination problem on interval graphs. The result is extended to solve the paired-domination problem on circular-arc graphs in O(m(m+ n)) time. MSC: 05C69, 05C85, 68Q25, 68R10, 68W05

Bipartite probe interval graphs, circular arc graphs, and interval point bigraphs

Linear-Time Algorithms for the Paired-Domination Problem in Interval Graphs and Circular-Arc Graphs

In a graph G, a vertex subset S ⊆ V (G) is said to be a dominating set of G if every vertex not in S is adjacent to a vertex in S. A dominating set S of a graph G is called a paired-dominating set if the induced subgraph G[S] contains a perfect matching. The paired-domination problem involves finding a smallest paired-dominating set of G. Given an intersection model of an interval graph G with ...