Set covering problem with conflict constraints

Saffari, Saeed; Fathi, Yahya

doi:10.1016/j.cor.2022.105763

Cited by 8 publications

(3 citation statements)

References 60 publications

(79 reference statements)

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“…From a more general perspective, various optimization problems on graphs were studied with the feature of an added conflict structure, e.g., [28,53,58]. Recently, [48] presented an interesting model for consistency in databases based on a conflict graph.…”

Section: Overview Of Related Workmentioning

confidence: 99%

Fair Allocation of Indivisible Items with Conflict Graphs

et al. 2022

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We consider the fair allocation of indivisible items to several agents and add a graph theoretical perspective to this classical problem. Namely, we introduce an incompatibility relation between pairs of items described in terms of a conflict graph. Every subset of items assigned to one agent has to form an independent set in this graph. Thus, the allocation of items to the agents corresponds to a partial coloring of the conflict graph. Every agent has its own profit valuation for every item. Aiming at a fair allocation, our goal is the maximization of the lowest total profit of items allocated to any one of the agents. The resulting optimization problem contains, as special cases, both Partition and Independent Set. In our contribution we derive complexity and algorithmic results depending on the properties of the given graph. We show that the problem is strongly NP-hard for bipartite graphs and their line graphs, and solvable in pseudo-polynomial time for the classes of chordal graphs, cocomparability graphs, biconvex bipartite graphs, and graphs of bounded treewidth. Each of the pseudo-polynomial algorithms can also be turned into a fully polynomial approximation scheme (FPTAS).

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Section: Overview Of Related Workmentioning

confidence: 99%

Fair Allocation of Indivisible Items with Conflict Graphs

et al. 2022

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“…The classic set covering model and set partition model are two model building approaches used to formulate the driver scheduling and crew rostering problems [11]. Such models aim to determine a work list, in which a driver is assigned to each bus under the given timetables and all clauses of the labor contract are satisfied [6].…”

Section: Introductionmentioning

confidence: 99%

Modeling the train manning problem for a massive rapid transit line

Wang,

Li,

Zheng

et al. 2024

Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024)

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This study proposes a practical train manning problem (TMP) for a bi-directional massive rapid transit (MRT) line with a certain number of crew points. The TMP aims to determine a set of manning duties for each rover to man the daily train services subjected to practical constraints by minimizing the total idle time of rovers. It is crucial for the MRT operators to solve the TMP because rovers are able to handle possible train faults and/or emergencies through their fast responses. In this paper, we build a binary nonlinear and nonconvex programming model with explicit constraints for the proposed TMP, by considering three possible train manning scenarios with different idle times. Moreover, we conduct a case study of the Singapore circle line and perform necessary sensitivity analysis of various parameters involved in the TMP. Results indicate that our model can solve the TMP problem effectively and the solutions help to improve the manning duties assignment.

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“…They name the problem Conflict-free Set Covering Problem and analyze it in the context of approximation algorithms and parametrized complexity. In Saffari and Fathi (2022), the authors introduce several families of valid inequalities for the Conflict-free Set Covering Problem and work out some pre-processing procedures to further speed up the problem resolution. The work also suggests interesting application contexts such as wireless communication services management and multi-period staff-scheduling problems.…”

Section: Introductionmentioning

confidence: 99%