Stavros D. Nikolopoulos

Addressing network survivability issues by finding the K-best paths through a trellis graph

Due to the increasing reliance of society on the timely and reliable transfer of large quantities of information (such as voice, data, and video) across high speed communication networks, it is becoming important for a network to offer survivability, or at least graceful degradation, in the event of network failure. In this paper we aim to offer a solution in the selection of the K-best disjoint paths through a network by using graph theoretic techniques. The basic approach is to map an arbitrary network graph into a trellis graph which allows the application of computationally efficient methods to find disjoint paths. Use of the knowledge of the K-best disjoint paths for improving the survivability of ATM networks at the virtual path and virtual circuit level is discussed.

The 1-Fixed-Endpoint Path Cover Problem is Polynomial on Interval Graphs

AbstractWe consider a variant of the path cover problem, namely, the k-fixed-endpoint path cover problem, or kPC for short, on interval graphs. Given a graph G and a subset

The Longest Path Problem Is Polynomial on Interval Graphs

\mathcal{T}

Encoding watermark integers as self-inverting permutations

of k vertices of V(G), a k-fixed-endpoint path cover of G with respect to

The Longest Path Problem Is Polynomial on Cocomparability Graphs

\mathcal{T}

The Number of Spanning Trees in K n -Complements of Quasi-Threshold Graphs

is a set of vertex-disjoint paths ℘ that covers the vertices of G such that the k vertices of

NP-completeness results for some problems on subclasses of bipartite and chordal graphs

\mathcal{T}

An Efficient Graph Codec System for Software Watermarking

are all endpoints of the paths in ℘. The kPC problem is to find a k-fixed-endpoint path cover of G of minimum cardinality; note that, if

The harmonious coloring problem is NP-complete for interval and permutation graphs

\mathcal{T}

Parallel algorithms for Hamiltonian problems on quasi-threshold graphs

is empty the stated problem coincides with the classical path cover problem. In this paper, we study the 1-fixed-endpoint path cover problem on interval graphs, or 1PC for short, generalizing the 1HP problem which has been proved to be NP-complete even for small classes of graphs. Motivated by a work of Damaschke (Discrete Math. 112:49–64, 1993), where he left both 1HP and 2HP problems open for the class of interval graphs, we show that the 1PC problem can be solved in polynomial time on the class of interval graphs. We propose a polynomial-time algorithm for the problem, which also enables us to solve the 1HP problem on interval graphs within the same time and space complexity.