Scheduling problems

  title={Scheduling problems},
  author={Felix Breuer and Caroline J. Klivans},
  journal={J. Comb. Theory, Ser. A},
Plurigraph Coloring and Scheduling Problems
A new type of vertex coloring is defined which generalizes vertex coloring in graphs, hypergraphs, and simplicial complexes and it is shown how the deletion-contraction law can be applied to scheduling problems.
Scheduling Problems and Generalized Graph Coloring
We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, andsimplicial complexes. To this coloring there is an associated symmetric function in noncommuting
Quasisymmetric and Schur expansions of cycle index polynomials
Abstract Given a subgroup G of the symmetric group S n , the cycle index polynomial cyc G is the average of the power-sum symmetric polynomials indexed by the cycle types of permutations in G . By
Hopf monoids and generalized permutahedra
Generalized permutahedra are a family of polytopes with a rich combinatorial structure and strong connections to optimization. We prove that they are the universal family of polyhedra with a certain
New invariants for permutations, orders and graphs
It is shown that the chromatic symmetric function and many other invariants have a property the authors call positively $h$-alternating, which leads to Schur positivity and e-positivity when applying the operator $\nabla$ at $q=1$.
Chromatic Symmetric Functions of Hypertrees
  • Jair Taylor
  • Mathematics, Computer Science
    Electron. J. Comb.
  • 2017
This work exhibits a class of hypergraphs, called hypertrees with prime-sized edges, for which X_H is positive in the fundamental quasisymmetric functions of F_S, and gives an explicit combinatorial interpretation for the F-coefficients ofX_H.
Resolving Stanley's $e$-positivity of claw-contractible-free graphs
In Stanley's seminal 1995 paper on the chromatic symmetric function, he stated that there was no known graph that was not contractible to the claw and whose chromatic symmetric function was not
Coupling a genetic algorithm with the distributed arrival-time control for the JIT dynamic scheduling of flexible job-shops
In order to increase customer satisfaction and competitiveness, manufacturing systems need to combine flexibility with Just-in-Time (JIT) production. Until now, research on JIT scheduling problems
Combinatorial Hopf Algebras of Simplicial Complexes
A family of combinatorial Hopf algebras are obtained by defining a family of characters on a Hopf algebra of simplicial complexes and using characters to give a generalization of Stanley's $(-1)$-color theorem.
The main part of the paper presents and discusses numerical experiments on industrial instances to show the benefit of choosing a suitable modeling for complex machines.


Approximation algorithms for scheduling unrelated parallel machines
It is proved that no polynomial algorithm can achieve a worst-case ratio less than 3/2 unlessP = NP, and a complexity classification for all special cases with a fixed number of processing times is obtained.
A Chromatic Symmetric Function in Noncommuting Variables
AbstractStanley (Advances in Math.111, 1995, 166–194) associated with a graph G a symmetric function XG which reduces to G's chromatic polynomial $${\mathcal{X}_G \left( n \right)}$$ under a
The Coloring Ideal and Coloring Complex of a Graph
Let G be a simple graph on d vertices. We define a monomial ideal K in the Stanley-Reisner ring A of the order complex of the Boolean algebra on d atoms. The monomials in K are in one-to-one
A Symmetric Function Generalization of the Chromatic Polynomial of a Graph
Abstract For a finite graph G with d vertices we define a homogeneous symmetric function XG of degree d in the variables x1, x2, ... . If we set x1 = ... = xn= 1 and all other xi = 0, then we obtain
A packing problem you can almost solve by sitting on your suitcase
In this paper, we present a novel approach for approximating solutions to the bin-packing and machine scheduling problems. In obtaining our results, we exploit a certain dual relationship that exists
A quasisymmetric function for matroids
This invariant defines a Hopf morphism from the Hopf algebra of matroids to the quasisymmetric functions, which is surjective if one uses rational coefficients and can sometimes be used to prove that a matroid base polytope has no decompositions into smaller matroidbase polytopes.
One-Processor Scheduling with Symmetric Earliness and Tardiness Penalties
It is shown that the problem of finding minimum cost schedules is NP-complete; however, an efficient algorithm is given that finds minimum cost scheduling whenever the tasks either all have the same length or are required to be executed in a given fixed sequence.
Scheduling Unrelated Machines by Randomized Rounding
We present a new class of randomized approximation algorithms for unrelated parallel machine scheduling problems with the average weighted completion time objective. The key idea is to assign jobs
Formulating the single machine sequencing problem with release dates as a mixed integer program
A hierarchy of relaxations obtained by combining enumeration of initial sequences with Smith's rule can be formulated as a linear programming problem in an enlarged space of variables and new valid inequalities for the problem are obtained.
A generalized permutation approach to job shop scheduling with genetic algorithms
In order to sequence the tasks of a job shop problem (JSP) on a number of machines related to the technological machine order of jobs, a new representation technique — mathematically known as