## 23 Citations

Plurigraph Coloring and Scheduling Problems

- Mathematics, Computer ScienceElectron. J. Comb.
- 2017

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

- Mathematics
- 2016

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

- Computer Science, MathematicsDiscret. Math.
- 2019

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

- Mathematics
- 2017

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

- Computer Science, MathematicsAdv. Appl. Math.
- 2020

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

- Mathematics, Computer ScienceElectron. 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

- Mathematics
- 2017

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

- Engineering
- 2014

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

- Mathematics, Computer ScienceSIAM J. Discret. Math.
- 2016

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.

A STUDY ON THE INTEGRATION OF COMPLEX MACHINES IN COMPLEX JOB SHOP SCHEDULING

- Computer Science2018 Winter Simulation Conference (WSC)
- 2018

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.

## References

SHOWING 1-10 OF 97 REFERENCES

Approximation algorithms for scheduling unrelated parallel machines

- Computer Science, Mathematics28th Annual Symposium on Foundations of Computer Science (sfcs 1987)
- 1987

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

- Mathematics
- 2001

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

- Mathematics
- 2001

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

- Mathematics
- 1995

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

- Mathematics
- 1986

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

- Mathematics, Computer ScienceEur. J. Comb.
- 2009

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

- Mathematics, Computer ScienceMath. Oper. Res.
- 1988

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

- Mathematics, Computer ScienceSIAM J. Discret. Math.
- 2002

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

- Computer Science, MathematicsDiscret. Appl. Math.
- 1990

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

- Mathematics
- 1995

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…