Related papers: A variant of multitask n-vehicle exploration probl…
The $n$-vehicle exploration problem (NVEP) is a nonlinear unconstrained optimization problem. Given a fleet of $n$ vehicles with mid-trip refueling technique, the NVEP tries to find a sequence of $n$ vehicles to make one of the vehicles…
The airplane refueling problem is a nonlinear combinatorial optimization problem, and its equivalent problem the $n$-vehicle exploration problem is proved to be NP-complete (arXiv:2304.03965v1, The $n$-vehicle exploration problem is…
The n-way number partitioning problem, a fundamental challenge in combinatorial optimization, has significant implications for applications such as fair division and machine scheduling. Despite these problems being NP-hard, many…
The Windows Scheduling Problem, also known as the Pinwheel Problem, is to schedule periodic jobs subject to their processing frequency demands. Instances are given as a set of jobs that have to be processed infinitely often such that the…
We consider the Maximum-Profit Routing Problem (MPRP), a variant of pick-up routing problem introduced in \cite{Armaselu-arXiv-2016, Armaselu-PETRA}, in which the goal is to maximize total profit. The original MPRP restricts vehicles to…
In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge…
We study the computational complexity of scheduling jobs on a single speed-scalable processor with the objective of capturing the trade-off between the (weighted) flow time and the energy consumption. This trade-off has been extensively…
Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…
We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In…
In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…
We consider several Vehicle Routing Problems (VRP) with profits, which seek to select a subset of customers, each one being associated with a profit, and to design service itineraries. When the sum of profits is maximized under distance…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
The profitable tour problem (PTP) is a well-known NP-hard routing problem searching for a tour visiting a subset of customers while maximizing profit as the difference between total revenue collected and traveling costs. PTP is known to be…
In this paper, we study the Maximum Profit Pick-up Problem with Time Windows and Capacity Constraint (MP-PPTWC). Our main results are 3 polynomial time algorithms, all having constant approximation factors. The first algorithm has an…
We study a scheduling problem in which jobs may be split into parts, where the parts of a split job may be processed simultaneously on more than one machine. Each part of a job requires a setup time, however, on the machine where the job…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
The computational complexity of the partition, 0-1 subset sum, unbounded subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple variants were studied in numerous papers in the past where all the weights and profits were…
The interval scheduling problem is one variant of the scheduling problem. In this paper, we propose a novel variant of the interval scheduling problem, whose definition is as follows: given jobs are specified by their {\em release times},…