@article {1425,
	title = {Decentralized decomposition algorithms for peer-to-peer linear optimization},
	journal = {RAIRO-Oper. Res.},
	volume = {54},
	year = {2020},
	pages = {1835-1861},
	doi = {10.1051/ro/2019097},
	url = {https://doi.org/10.1051/ro/2019097},
	author = {Aydin, M. Asli and Z C Ta{\c s}k{\i}n}
}
@article {1431,
	title = {A decomposition approach to solve the selective graph coloring problem in some perfect graph families},
	journal = {Networks},
	volume = {73},
	year = {2019},
	pages = {145-169},
	abstract = {<p>Graph coloring is the problem of assigning a minimum number of colors to all vertices of a graph such that no two adjacent vertices receive the same color. The selective graph coloring problem is a generalization of the standard graph coloring problem; given a graph with a partition of its vertex set into clusters, the objective is to choose exactly one vertex per cluster so that, among all possible selections, the number of colors necessary to color the vertices in the selection is minimum. This study focuses on a decomposition based exact solution framework for selective coloring in some perfect graph families: in particular, permutation, generalized split, and chordal graphs where the selective coloring problem is known to be NP-hard. Our method combines integer programming techniques and combinatorial algorithms for the graph classes of interest. We test our method on graphs with different sizes and densities, present computational results and compare them with solving an integer programming formulation of the problem by CPLEX, and a state-of-the art algorithm from the literature. Our computational experiments indicate that our decomposition approach significantly improves solution performance in low-density graphs, and regardless of edge-density in the class of chordal graphs.</p>},
	keywords = {chordal graphs, decomposition algorithm, generalized split graphs, integer programming, partition coloring, permutation graphs, selective graph coloring},
	doi = {https://doi.org/10.1002/net.21850},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/net.21850},
	author = {{\c S}eker, Oylum and Ekim, Tinaz and Z C Ta{\c s}k{\i}n}
}
@article {1432,
	title = {The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)},
	journal = {European Journal of Operational Research},
	volume = {272},
	year = {2019},
	pages = {372-388},
	abstract = {<p>The success of radiation therapy depends on the ability to deliver the proper amount of radiation to cancerous cells while protecting healthy tissues. As a natural consequence, any new treatment technology improves quality standards concerning primarily this issue. Similar to the widely used Intensity Modulated Radiation Therapy (IMRT), the radiation resource is outside of the patient{\textquoteright}s body and the beam is shaped by a multi-leaf collimator mounted on the linear accelerator{\textquoteright}s head during the state-of-the-art Volumetric Modulated Arc Therapy (VMAT) as well. However, unlike IMRT, the gantry of the accelerator may rotate along one or more arcs and deliver radiation continuously. This property makes VMAT powerful in obtaining high conformal plans in terms of dose distribution; but the apertures are interdependent and optimal treatment planning problem cannot be decomposed into simpler independent subproblems as a consequence. In this work, we consider optimal treatment planning problem for VMAT. First, we formulate a mixed-integer linear program minimizing total radiation dose intensity subject to clinical requirements embedded within the constraints. Then, we develop efficient solution procedures combining Benders decomposition with certain acceleration strategies. We investigate their performance on a large set of test instances obtained from an anonymous real prostate cancer data.</p>},
	keywords = {algorithms, Benders decomposition, integer programming, Radiation therapy, VMAT},
	issn = {0377-2217},
	doi = {https://doi.org/10.1016/j.ejor.2018.06.023},
	url = {https://www.sciencedirect.com/science/article/pii/S0377221718305514},
	author = {P{\i}nar Dursun and Z C Ta{\c s}k{\i}n and I. Kuban Altinel}
}
@article {BodurEtAl2013,
	title = {Decomposition Algorithms for Solving the Minimum Weight Maximal Matching Problem},
	journal = {Networks},
	volume = {62},
	number = {4},
	year = {2013},
	pages = {273{\textendash}287},
	doi = {http://dx.doi.org/10.1002/net.21516},
	author = {Merve Bodur and Ekim, Tinaz and Z C Ta{\c s}k{\i}n}
}
