Related papers: Exact and Approximate High-Multiplicity Scheduling…
We consider the bin packing problem with $d$ different item sizes and revisit the structure theorem given by Goemans and Rothvo\ss [6] about solutions of the integer cone. We present new techniques on how solutions can be modified and give…
With the rapid advancement of technology, parallel computing applications have become increasingly popular and are commonly executed in large data centers. These applications involve two phases: computation and communication, which are…
The lower and the upper irredundance numbers of a graph $G$, denoted $ir(G)$ and $IR(G)$ respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a…
We consider so-called $N$-fold integer programs (IPs) of the form $\max\{c^T x : Ax = b, \ell \leq x \leq u, x \in \mathbb Z^{nt}\}, where $A \in \mathbb Z^{(r+sn)\times nt} consists of $n$ arbitrary matrices $A^{(i)} \in \mathbb Z^{r\times…
Predicting the runtime complexity of a programming code is an arduous task. In fact, even for humans, it requires a subtle analysis and comprehensive knowledge of algorithms to predict time complexity with high fidelity, given any code. As…
We study the problem of preemptive scheduling n jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. We show that when all jobs have equal processing times then the problem can…
The pooling problem is an important industrial problem in the class of network flow problems for allocating gas flow in pipeline transportation networks. For P-formulation of the pooling problem with time discretization, we propose second…
Recently, the makespan-minimization problem of compiling a general class of quantum algorithms into near-term quantum processors has been introduced to the AI community. The research demonstrated that temporal planning is a strong approach…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
In this paper we consider the problem of scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of…
The problem of scheduling conflicting jobs on parallel machines consists in assigning a set of jobs to a set of machines so that no two conflicting jobs are allocated to the same machine, and the maximum processing time among all machines…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
This paper addresses the problem of scheduling jobs on identical machines with conflict constraints, where certain jobs cannot be scheduled simultaneously on different machines. We focus on the case where conflicts can be represented by a…
This paper studies the growing domain of Robotic Process Automation (RPA) problems. Motivated by scheduling problems arising in RPA, we study the parameterized complexity of the single-machine problem $1|\text{prec},r_j,d_j|*$. We focus on…
The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating…
We develop a general framework for finding approximately-optimal preconditioners for solving linear systems. Leveraging this framework we obtain improved runtimes for fundamental preconditioning and linear system solving problems including…
In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $\epsilon>0$, such algorithmic…
In the Scheduling Machines with Capacity Constraints problem, we are given k identical machines, each of which can process at most m_i jobs. M jobs are also given, where job j has a non-negative processing time length t_j >= 0. The task is…
An important goal in algorithm design is determining the best running time for solving a problem (approximately). For some problems, we know the optimal running time, assuming certain conditional lower bounds. In this work, we study the…