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Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we…

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 algorithm of Shor for prime factorization is a hybrid algorithm consisting of a quantum part and a classical part. The main focus of the classical part is a continued fraction analysis. The presentation of this is often short, pointing…

The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…

For constrained, not necessarily monotone submodular maximization, all known approximation algorithms with ratio greater than $1/e$ require continuous ideas, such as queries to the multilinear extension of a submodular function and its…

In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…

We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…

We consider the problem of solving integer programs of the form $\min \{\,c^\intercal x\ \colon\ Ax=b, x\geq 0\}$, where $A$ is a multistage stochastic matrix in the following sense: the primal treedepth of $A$ is bounded by a parameter…

The concept of p-ordering for a prime p was introduced by Manjul Bhargava (in his PhD thesis) to develop a generalized factorial function over an arbitrary subset of integers. This notion of p-ordering provides a representation of…

We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…

In this paper, first we give a sequential linear-time algorithm for the longest path problem in meshes. This algorithm can be considered as an improvement of [13]. Then based on this sequential algorithm, we present a constant-time parallel…

The goal of diagnosis is to compute good repair strategies in response to anomalous system behavior. In a decision theoretic framework, a good repair strategy has low expected cost. In a general formulation of the problem, the computation…

This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…

In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…

We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…

In the matroid partitioning problem, we are given $k$ matroids $\mathcal{M}_1 = (V, \mathcal{I}_1), \dots , \mathcal{M}_k = (V, \mathcal{I}_k)$ defined over a common ground set $V$ of $n$ elements, and we need to find a partitionable set $S…

In this paper, two approximation algorithms are given. Let N be an odd composite number. The algorithms give new directions regarding primality test of given N. The first algorithm is given using a new method called digital coding method.…

Leveraging planning during learning and decision-making is central to the long-term development of intelligent agents. Recent works have successfully combined tree-based search methods and self-play learning mechanisms to this end. However,…

We investigate an optimization problem in a queueing system where the service provider selects the optimal service fee p and service capacity \mu to maximize the cumulative expected profit (the service revenue minus the capacity cost and…

An optimal solution to the problem of scheduling real-time tasks on a set of identical processors is derived. The described approach is based on solving an equivalent uniprocessor real-time scheduling problem. Although there are other…