New Challenges in Combinatorial Optimization - Chen, Bo; Kulikov, Alexander; Martello, Silvano (Journal of combinatorial optimization, 2025)
Given an undirected, loopless and connected graph G, an optical spectrum of available contiguous frequency slots, and a set of traffic demands, the constrained-routing and spectrum assignment problem is to assign, to each traffic demand, a path in G between its origin and destination and a subset of contiguous frequency slots, subject to certain technological constraints, while optimizing a linear objective function. Péter Györgyi, Tamás Kis, and Tímea Tamási consider the online variant of a combination of the joint replenishment problem with single machine scheduling. [...]they show that, for a certain class of inputs , the competitive ratio of the algorithm tends to 2 as the number of jobs tends to infinity, and derive lower bounds for the best competitive ratio of any deterministic online algorithm under various assumptions. Alain Hertz, Sébastien Bonte, Gauvain Devillez, and Hadrien Mélot study the asymptotic behavior of the ratio of the average size of a maximal matching to the size of a maximum matching in a given graph. Selection of suppliers, location of warehouses, assigning of located warehouses to selected suppliers, and inventory control parameters for each selected warehouse are considered.