45 research outputs found
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
An Algorithmic Framework for Locally Constrained Homomorphisms
A homomorphism φ from a guest graph G to a host graph H
is locally bijective, injective or surjective if for every u ∈ V (G), the
restriction of φ to the neighbourhood of u is bijective, injective or
surjective, respectively. The corresponding decision problems, LBHom,
LIHom and LSHom, are well studied both on general graphs and on
special graph classes. We prove a number of new FPT, W[1]-hard and
para-NP-complete results by considering a hierarchy of parameters of
the guest graph G. For our FPT results, we do this through the development of a new algorithmic framework that involves a general ILP model.
To illustrate the applicability of the new framework, we also use it to
prove FPT results for the Role Assignment problem, which originates
from social network theory and is closely related to locally surjective
homomorphisms
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization
International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM
Mathematical Models and Decomposition Algorithms for Cutting and Packing Problems
In this thesis, we provide (or review) new and effective algorithms based on Mixed-Integer Linear Programming (MILP) models and/or decomposition approaches to solve exactly various cutting and packing problems.
The first three contributions deal with the classical bin packing and cutting stock problems. First, we propose a survey on the problems, in which we review more than 150 references, implement and computationally test the most common methods used to solve the problems (including
branch-and-price, constraint programming (CP) and MILP), and we successfully propose new instances that are difficult to solve in practice. Then, we introduce the BPPLIB, a collection of codes, benchmarks, and links for the two problems. Finally, we study in details the main MILP formulations that have been proposed for the problems, we provide a clear picture of the dominance and equivalence relations that exist among them, and we introduce reflect, a new pseudo-polynomial formulation that achieves state of the art results for both problems and some variants.
The following three contributions deal with two-dimensional packing problems. First, we propose a method using Logic based Benders’ decomposition for the orthogonal stock cutting problem and some extensions. We solve the master problem through an MILP model while CP is used to solve the slave problem. Computational experiments on classical benchmarks from the literature show the effectiveness of the proposed approach. Then, we introduce TwoBinGame, a visual application we developed for students to interactively solve two-dimensional packing problems, and analyze the results obtained by 200 students. Finally, we study a complex optimization problem that originates from the packaging industry, which combines cutting and scheduling decisions. For its solution, we propose mathematical models and heuristic algorithms that involve a non-trivial decomposition method.
In the last contribution, we study and strengthen various MILP and CP approaches for three project scheduling problems