11 research outputs found
Minimum Cost Homomorphisms to Reflexive Digraphs
For digraphs and , a homomorphism of to is a mapping $f:\
V(G)\dom V(H)uv\in A(G)f(u)f(v)\in A(H)u \in V(G)c_i(u), i \in V(H)f\sum_{u\in V(G)}c_{f(u)}(u)H, the {\em minimum cost homomorphism problem} for HHGc_i(u)u\in V(G)i\in V(H)kGHk. We focus on the
minimum cost homomorphism problem for {\em reflexive} digraphs HHHH has a {\em Min-Max ordering}, i.e.,
if its vertices can be linearly ordered by <i<j, s<rir, js
\in A(H)is \in A(H)jr \in A(H)H$ which does not admit a Min-Max ordering, the minimum cost
homomorphism problem is NP-complete. Thus we obtain a full dichotomy
classification of the complexity of minimum cost homomorphism problems for
reflexive digraphs
Minimum Cost Homomorphisms to Locally Semicomplete and Quasi-Transitive Digraphs
For digraphs and , a homomorphism of to is a mapping $f:\
V(G)\dom V(H)uv\in A(G)f(u)f(v)\in A(H)u \in V(G)c_i(u), i \in V(H)f\sum_{u\in V(G)}c_{f(u)}(u)HHHGc_i(u)u\in V(G)i\in V(H)GH$ and, if one exists, to find one of minimum cost.
Minimum cost homomorphism problems encompass (or are related to) many well
studied optimization problems such as the minimum cost chromatic partition and
repair analysis problems. We focus on the minimum cost homomorphism problem for
locally semicomplete digraphs and quasi-transitive digraphs which are two
well-known generalizations of tournaments. Using graph-theoretic
characterization results for the two digraph classes, we obtain a full
dichotomy classification of the complexity of minimum cost homomorphism
problems for both classes
A branch-and-price algorithm for a hierarchical crew scheduling problem.
We describe a real-life problem arising at a crane rental company. This problem is a generalization of the basic crew scheduling problem given in Mingozzi et al. and Beasley and Cao. We formulate the problem as an integer programming problem and establish ties with the integer multicommodity flow problem and the hierarchical interval scheduling problem. After establishing the complexity of the problem we propose a branch-and-price algorithm to solve it. We test this algorithm on a limited number of real-life instances.Scheduling;
Departure Management with Robust Gate Allocation
International audienceThe Airport Collaborative Decision Making (A-CDM) concept yields concrete and promising solutions for airports, in terms of traffic punctuality and predictability, with possible delay, noise and pollution reduction. A key feature of A-CDM is the Departure Management (DMAN): runway takeoff sequences can be anticipated such that a significant part of the delay can be shifted at the gate, engines off, without penalizing the remaining traffic. During this process, an increase in the gate occupancy for delayed departures is unavoidable, therefore the airport layout must provide enough gates and their allocation must be robust enough w.r.t. departures delay. In this paper, we introduce a method to estimate the gate delays due to the DMAN pre-departure scheduling, then we propose a robust gate allocation algorithm and assess its performance with current and increased traffic at Paris-Charles-de-Gaulle international airport. Results show a significant reduction in the number of gate conflicts, when comparing such a robust gate allocation to current practice
Interval Scheduling: A Survey
In interval scheduling, not only the processing times of the jobs but also their starting times are given. This article surveys the area of interval scheduling and presents proofs of results that have been known within the community for some time. We first review the complexity and approximability of different variants of interval scheduling problems. Next, we motivate the relevance of interval scheduling problems by providing an overview of applications that have appeared in literature. Finally, we focus on algorithmic results for two important variants of interval scheduling problems. In one variant we deal with nonidentical machines: instead of each machine being continuously available, there is a given interval for each machine in which it is available. In another variant, the machines are continuously available but they are ordered, and each job has a given "maximal" machine on which it can be processed. We investigate the complexity of these problems and describe algorithms for their solution
A Unified Framework for Integer Programming Formulation of Graph Matching Problems
Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been formulated as a mathematical program then solved using exact, heuristic and/or approximated-guaranteed procedures. On the other hand, graph theory has been a powerful tool in visualizing and understanding of complex mathematical programming problems, especially integer programs. Formulating a graph problem as a natural integer program (IP) is often a challenging task. However, an IP formulation of the problem has many advantages. Several researchers have noted the need for natural IP formulation of graph theoretic problems. The aim of the present study is to provide a unified framework for IP formulation of graph matching problems. Although there are many surveys on graph matching problems, however, none is concerned with IP formulation. This paper is the first to provide a comprehensive IP formulation for such problems. The framework includes variety of graph optimization problems in the literature. While these problems have been studied by different research communities, however, the framework presented here helps to bring efforts from different disciplines to tackle such diverse and complex problems. We hope the present study can significantly help to simplify some of difficult problems arising in practice, especially in pattern analysis