Related papers: Scheduling Problems
A function that is analytic on a domain of $\mathbb{C}^n$ is holonomic if it is the solution to a holonomic system of linear homogeneous differential equations with polynomial coefficients. We define and study the Bernstein-Sato polynomial…
We consider the classic problem of scheduling jobs with precedence constraints on identical machines to minimize makespan, in the presence of communication delays. In this setting, denoted by $\mathsf{P} \mid \mathsf{prec}, c \mid…
An arrangement of $n$ curves in the plane is given. The query is a point $q$ and the goal is to find the face of the arrangement that contains $q$. A data-structure for point-location, preprocesses the curves into a data structure of…
Stanley associated with a graph G a symmetric function X_G which reduces to G's chromatic polynomial under a certain specialization of variables. He then proved various theorems generalizing results about the chromatic polynomial, as well…
Many planning formalisms allow for mixing numeric with Boolean effects. However, most of these formalisms are undecidable. In this paper, we will analyze possible causes for this undecidability by studying the number of different…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
Schaefer introduced a framework for generalized satisfiability problems on the Boolean domain and characterized the computational complexity of such problems. We investigate an algebraization of Schaefer's framework in which the Fourier…
Motivated by modern parallel computing applications, we consider the problem of scheduling parallel-task jobs with heterogeneous resource requirements in a cluster of machines. Each job consists of a set of tasks that can be processed in…
Motivated by fairness concerns, we study the `portfolio problem': given an optimization problem with set $D$ of feasible solutions, a class $\mathbf{C}$ of fairness objective functions on $D$, and an approximation factor $\alpha \ge 1$, a…
In this paper, we study the active time scheduling problem. We are given n jobs with integral processing times each of which has an integral release time and deadline. The goal is to schedule all the jobs on a machine that can work on b…
A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in $\mathsf{P}$ or $\mathsf{NP}$-hard. This paper considers a promise-problem variant of CSPs called…
A Stein manifold X is called S-parabolic if it possesses a plurisub- harmonic exhaustion function p that is maximal outside a compact subset of X: In analogy with (Cn; ln jzj), one defines the space of polynomials on a S- parabolic manifold…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
Malleable scheduling is a model that captures the possibility of parallelization to expedite the completion of time-critical tasks. A malleable job can be allocated and processed simultaneously on multiple machines, occupying the same time…
We study shared multi-processor scheduling problem where each job can be executed on its private processor and simultaneously on one of many processors shared by all jobs in order to reduce the job's completion time due to processing time…
The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications.…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence…
Semi-bent Boolean functions are interesting from a cryptographic standpoint, since they possess several desirable properties such as having a low and flat Walsh spectrum, which is useful to resist linear cryptanalysis. In this paper, we…
The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its…