The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
Coloring planar graphs in parallel
Journal of Algorithms
Information Processing Letters
Fast parallel algorithms for chordal graphs
SIAM Journal on Computing
An optimal greedy heuristic to color interval graphs
Information Processing Letters
Optimal parallel 3-coloring algorithm for rooted trees and its application
Information Processing Letters
Optimal parallel time bounds for the maximum clique problem on intervals
Information Processing Letters
A simple linear time algorithm for triangulating three-colored graphs
Journal of Algorithms
Ranking fuzzy interval numbers in the setting of random sets
Information Sciences: an International Journal
A still better performance guarantee for approximate graph coloring
Information Processing Letters
Ranking fuzzy interval numbers in the setting of random sets — further results
Information Sciences: an International Journal
An Efficient Algorithm for Finding a Maximum Weight k-Independent Set on Trapezoid Graphs
Computational Optimization and Applications
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
Independent Sets in Asteroidal Triple-Free Graphs
SIAM Journal on Discrete Mathematics
A Coloring Algorithm for Interval Graphs
MFCS '89 Proceedings on Mathematical Foundations of Computer Science 1989
Optimal Parallel Algorithms For The Recognition And Colouring Outerplanar Graphs (Extended Abstract)
MFCS '89 Proceedings on Mathematical Foundations of Computer Science 1989
Logarithmic Time NC Algorithms for Comparability Graphs and Circle Graphs
ICCI '91 Proceedings of the International Conference on Computing and Information: Advances in Computing and Information
Fast Parallel Algorithms for Cographs
Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science
The mutual exclusion scheduling problem for permutation and comparability graphs
Information and Computation
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
On arithmetic operations of interval numbers
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Aliased register allocation for straight-line programs is NP-complete
Theoretical Computer Science
Information Sciences: an International Journal
A decoupled local memory allocator
ACM Transactions on Architecture and Code Optimization (TACO) - Special Issue on High-Performance Embedded Architectures and Compilers
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The present paper aims at developing a linear time algorithm to find a solution to the 'maximum weight 1 colouring' problem for an interval graph with interval weight. This algorithm has been applied to solve the problem that involves selecting different programme slots telecast on different television channels in a day so as to reach the maximum number of viewers. It is shown that all programmes of all television channels can be modelled as a weighted interval graph with interval numbers as weights. The programme slots are taken as the vertices of the graph and if the time durations of two programme slots have non-empty intersection, the corresponding vertices are considered to be connected by an edge. The number of viewers of a programme is taken as the weight of the vertex. In reality, the number of viewers of a programme is not a fixed one; generally, it lies in an interval. Thus, the weights of the vertices are taken as interval numbers. We assume that a company sets the objective of selecting the popular programme in different channels so as to make its commercial advertisement reach the maximum number of viewers. However, the constraint imposed is that all selected programmes are mutually exclusive in respect of time scheduling. The objective of the paper is, therefore, to helps the companies to select the programme slots, which are mutually exclusive with respect to the time schedule of telecasting time, in such a way that the total number of viewers of the selected programme slots rises to the optimum level. It is shown that the solution of this problem is obtained by solving the maximum weight colouring problem on an interval graph. An algorithm is designed to solve this optimization problem using O(n) time, where n represents the total number of programmes of all channels.