Linear algorithm for optimal path cover problem on interval graphs
Information Processing Letters
Optimal covering of cacti by vertex-disjoint paths
Theoretical Computer Science
Optimal path cover problem on block graphs and bipartite permutation graphs
Theoretical Computer Science
On the complexity of coupled-task scheduling
Discrete Applied Mathematics - Special issue on models and algorithms for planning and scheduling problems
Advances on the Hamiltonian Completion Problem
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A time-optimal solution for the path cover problem on cographs
Theoretical Computer Science
A linear algorithm for the Hamiltonian completion number of the line graph of a cactus
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
8/7-approximation algorithm for (1,2)-TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Finding a minimum path cover of a distance-hereditary graph in polynomial time
Discrete Applied Mathematics
Solving the path cover problem on circular-arc graphs by using an approximation algorithm
Discrete Applied Mathematics
| Hi-index | 0.00 |
The problem presented in this paper is a generalization of the usual coupled-tasks scheduling problem in presence of compatibility constraints. The reason behind this study is the data acquisition problem for a submarine torpedo. We investigate a particular configuration for coupled tasks (any task is divided into two sub-tasks separated by an idle time), in which the idle time of a coupled task is equal to the sum of durations of its two sub-tasks. We prove $\mathcal{NP}$ -completeness of the minimization of the schedule length, we show that finding a solution to our problem amounts to solving a graph problem, which in itself is close to the minimum-disjoint-path cover (min-DCP) problem. We design a $(\frac{3a+2b}{2a+2b})$ -approximation, where a and b (the processing time of the two sub-tasks) are two input data such as ab0, and that leads to a ratio between $\frac {3}{2}$ and $\frac{5}{4}$ . Using a polynomial-time algorithm developed for some class of graph of min-DCP, we show that the ratio decreases to $\frac{1+\sqrt{3}}{2}\approx 1.37$ .