Optimal parallel algorithms for the recognition and colouring outerplanar graphs

Diks, Krzysztof; Hagerup, Torben; Rytter, Wojciech

doi:10.1007/3-540-51486-4_68

Cited by 5 publications

(4 citation statements)

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“…We assume that all vertices in G o are named consecutively in clockwise order around the exterior face and the tree of faces inĜ o is binary. According to [4,19] the construction of the tree of faces and its binarization, as well as the consecutive naming of the vertices in G o can be achieved in O(log n log * n) time using O(n/ log n log * n) CREW PRAM processors. (More details in [12].…”

Section: An Optimal Work Algorithm For Detecting Negative Cycles In Omentioning

confidence: 99%

Efficient sequential and parallel algorithms for the negative cycle problem

Kavvadias

Pantziou

Spirakis

et al. 1994

Algorithms and Computation

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Section: An Optimal Work Algorithm For Detecting Negative Cycles In Omentioning

confidence: 99%

Efficient sequential and parallel algorithms for the negative cycle problem

Kavvadias

Pantziou

Spirakis

et al. 1994

Algorithms and Computation

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“…Chordal graphs [2,4,18,32,46], interval graphs [15,16,17,33,44], planar graphs [5], outer planar graphs [9], trees [38], etc. are such classes.…”

Section: Survey Of Related Workmentioning

confidence: 99%

“…(1), c 2 = (2, 3, 4), c 3 = (5, 6, 7), c 4 =(8,9,10), c 5 = (10, 11, 12), c 6 = (13, 14, 15),c 7 = (15, 16, 17), c 8 = (18, 20, 25), c 9 = (19, 20, 25), c 10 = (21, 22, 25), c 11 = (22, 23, 25), c 12 = (24, 25, 26), c 13 = (25, 26, 27), c 14 = (27, 29, 32), c 15 = (28, 29, 32), c 16 = (30, 31, 32), c 17 = (32, 33, 34), c 18 = (34, 35, 36), c 19 = (37, 38, 41), c 20 = (39, 40, 41), c 21 = (42, 43, 44), c 22 = (43, 44, 45), c 23 = (45, 46), c 24 = (46, 47, 50), c 25 = (47, 48, 50), c 26 = (48, 49, 50), c 27 = (50, 51, 52), c 28 = (52, 53, 54).…”

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confidence: 99%

Scheduling Algorithm to Select Optimal Programme Slots in Television Channels: A Graph Theoretic Approach

Pal

2016

Int. J. Appl. Comput. Math

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In this paper, it is shown that all programmes of all television channels can be modelled as an interval graph. The programme slots are taken as the vertices of the graph and if the time duration 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. A set of programmes that are mutually exclusive in respect of time scheduling is called a session. We assume that a company sets the objective of selecting the popular programmes in k parallel sessions among different channels so as to make its commercial advertisement reach the maximum number of viewers, that is, a company selects k suitable programme slots simultaneously for advertisement. The aim of the paper is, therefore, to help 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 in k parallel slots rises to the optimum level. It is shown that the solution of this problem is obtained by solving the maximum weight k-colouring problem on an interval graph.An algorithm is designed to solve this just-in-time optimization problem using O(kM n 2 ) time, where n and M represent the total number of programmes of all channels and the upper bound of the viewers of all programmes of all channels respectively. The problem considered in this paper is a daily life problem which is modeled by k-colouring problem on interval graph.

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“…A great deal of research has been done to identify classes of graphs for which these problems are solvable in polynomial time. The identified classes are chordal graphs [1,2,21,28,39], circular-arc graphs [27], interval graphs [15,16,19,30,37], rectangle intersection graphs [6], planar graphs [3], comparability graphs [9], circle graphs [9], cographs [26], outer planar graph [12], tree [33], asteroidal triple free graphs [4], etc. The maximum-weight independent set and maximum-weight k-independent set problems are also studied on many graphs classes like permutation graphs [34,35], trapezoid graphs [23], etc.…”

Section: Introductionmentioning

confidence: 99%