Martín Matamala

The pickup and delivery problem with transfers: Formulation and a branch-and-cut solution method

In this paper, a strict formulation of a generalization of the classical pickup and delivery problem is presented. Here, we add the flexibility of providing the option for passengers to transfer from one vehicle to another at specific locations. As part of the mathematical formulation, we include transfer nodes where vehicles may interact interchanging passengers. Additional variables to keep track of customers along their route are considered. The formulation has been proven to work correctly, and by means of a simple example instance, we conclude that there exist some configurations in which a scheme allowing transfers results in better quality optimal solutions. Finally, a solution method based on Benders decomposition is addressed. We compare the computational effort of this application with a straight branch and bound strategy; we also provide insights to develop more efficient set partitioning formulations and associated algorithms for solving real-size problems.

Reconstructing 3-Colored Grids from Horizontal and Vertical Projections Is NP-hard

We consider the problem of coloring a grid using k colors with the restriction that in each row and each column has an specific number of cells of each color. In an already classical result, Ryser obtained a necessary and sufficient condition for the existence of such a coloring when two colors are considered. This characterization yields a linear time algorithm for constructing such a coloring when it exists. Gardner et al. showed that for k ≥ 7 the problem is NP-hard. Afterward Chrobak and Durr improved this result, by proving that it remains NP-hard for k ≥ 4. We solve the gap by showing that for 3 colors the problem is already NP-hard. Besides we also give some results on tiling tomography.

Reconstructing 3-Colored Grids from Horizontal and Vertical Projections is NP-Hard: A Solution to the 2-Atom Problem in Discrete Tomography

We consider the problem of coloring a grid using

Small alliances in graphs

k

AT-free graphs: linear bounds for the oriented diameter

colors with the restriction that each row and each column has a specific number of cells of each color. This problem has been known as the

Recursive construction of periodic steady state for neural networks

(k-1)

Solving the Induced Subgraph Problem in the Randomized Multiparty Simultaneous Messages Model

-atom problem in the discrete tomography community. In an already classical result, Ryser obtained a necessary and sufficient condition for the existence of such a coloring when two colors are considered. This characterization yields a linear time algorithm for constructing such a coloring when it exists. Gardner et al. showed that for

Alternation on cellular automata

k\geqslant 7

Complexity and dimension

the problem is NP-hard. Afterward Chrobak and Durr improved this result by proving that it remains NP-hard for

Allowing each node to communicate only once in a distributed system: shared whiteboard models

k\geqslant 4