Journal Article10.1080/00207169608804486
A sequential algorithm for finding a maximum weight K-independent set on interval graphs
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TL;DR: Using this algorithm the maximum weight 2-independent set problem for an interval graph with n vertices can be solved in O(n √logc + γ) time.
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Abstract: In this paper an O(kn√logc+γ) time algorithm is presented to solve the maximum weight k-independent set problem on an interval graph with n vertices and non-negative integer weights, where c is the weight of the longest path of the interval graph and γ is the total size of all maximal cliques, given its interval representation. If the intervals are not sorted then considering the time for sorting the time complexity is of O(nlogn+kn √logc+γ). Using this algorithm the maximum weight 2-independent set problem for an interval graph with n vertices can be solved in O(n √logc + γ) time. The best known previous algorithm for 2-independent set problem requires O(n 2) time.
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Citations
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The just-in-time scheduling problem in a flow-shop scheduling system ☆
TL;DR: The problem of maximizing the weighted number of just-in-time (JIT) jobs in a flow-shop scheduling system under four different scenarios is studied and it is shown that the time complexity can be reduced to O(nlogn) if all the jobs have the same gain for being completed JIT.
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Maximizing the weighted number of just-in-time jobs in several two-machine scheduling systems
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TL;DR: A pseudo-polynomial time algorithm is provided to solve the problem of maximizing the weighted number of just-in-time jobs in a two-machine flow shop scheduling system, proving that it is $\mathcal{NP}$-hard in the ordinary sense.
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An Efficient Algorithm for Finding a Maximum Weight k-Independent Set on Trapezoid Graphs
TL;DR: An O(kn2) time sequential algorithm is designed in this paper to solve the maximum weight k-independent set problem on weighted trapezoid graphs.
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L(2,1)-labeling of interval graphs
TL;DR: In this paper, it was shown that λ2,1(G) ≤ � + 3ω for circular-arc graphs, where m and n represent the number of edges and vertices respectively.
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