Related papers: An algebraic approach to project schedule developm…
We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…
In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…
Scheduling precedence-constrained tasks under shared renewable resources is central to modern computing platforms. The Resource Investment Problem (RIP) models this setting by minimizing the cost of provisioned renewable resources under…
This paper presents an integer programming-based optimization framework designed to effectively address the complex final exam scheduling challenges encountered at Cornell University. With high flexibility, the framework is specifically…
As Grid computing is becoming an inevitable future, managing, scheduling and monitoring dynamic, heterogeneous resources will present new challenges. Solutions will have to be agile and adaptive, support self-organization and autonomous…
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
In a warehouse environment, tasks appear dynamically. Consequently, a task management system that matches them with the workforce too early (e.g., weeks in advance) is necessarily sub-optimal. Also, the rapidly increasing size of the action…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
This survey aims at demonstrating that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed many problems can be NP-hard when considering general precedence constraints, while they…
A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize \v{C}ech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\mathbb{P}^n_M$, a projective…
With an ever growing number of heterogeneous applicational services running on equally heterogeneous computational systems, the problem of resource management becomes more essential. Although current solutions consider some network and time…
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically,…
We represent vector bundles over a regular algebraic curve as pairs of lattices over the maximal orders of its function field and we give polynomial time algorithms for several tasks: computing determinants of vector bundles, kernels and…
An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric…
In process algebras such as ACP (Algebra of Communicating Processes), parallel processes are considered to be interleaved in an arbitrary way. In the case of multi-threading as found in contemporary programming languages, parallel processes…
A new class of representations of the Brauer algebra that centralizes the action of orthogonal and symplectic groups in tensor spaces is found. These representations make it possible to apply the technique of building primitive orthogonal…
This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project…
We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…
The manpower scheduling problem is a kind of critical combinational optimization problem. Researching solutions to scheduling problems can improve the efficiency of companies, hospitals, and other work units. This paper proposes a new model…
Abstract algebra provides a large hierarchy of properties that a collection of objects can satisfy, such as forming an abelian group or a semiring. These classifications can arranged into a broad and typically acyclic directed graph. This…