Related papers: Asymmetric Number Partitioning with Splitting and …
Given a tree $T$ on $n$ vertices, and $k, b, s_1, \ldots, s_b \in N$, the Tree Partitioning problem asks if at most $k$ edges can be removed from $T$ so that the resulting components can be grouped into $b$ groups such that the number of…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…
We consider the equal sum partition problem, motivated by distance magic graph labeling: Given $n,k \in \N$ such that $k\, | \sum_{i=1}^ni$ and a partition $p_1+\cdots+p_k=n$, when is it possible to find a partition of the set…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
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 explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
We present a polynomial time algorithm, which solves a nonstandard Variation of the well-known PARTITION-problem: Given positive integers $n, k$ and $t$ such that $t \geq n$ and $k \cdot t = {n+1 \choose 2}$, the algorithm partitions the…
Resource allocation problems in which demand is splittable are usually solved using different solution methods from their unsplittable equivalents. Although splittable problem instances can be the easier of the two (for example, they might…
We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on…
Given an $n$-point metric space $(\mathcal{X},d)$ where each point belongs to one of $m=O(1)$ different categories or groups and a set of integers $k_1, \ldots, k_m$, the fair Max-Min diversification problem is to select $k_i$ points…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
This article studies the problem of modifying the action ordering of a plan in order to optimise the plan according to various criteria. One of these criteria is to make a plan less constrained and the other is to minimize its parallel…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, the problems need to be formulated as unconstrained binary models, taking…
In a recent paper, Brusco, K\"ohn and Steinley [Ann. Oper. Res. 206:611-626 (2013)] conjecture that the 2 bins special case of the one-dimensional minimax bin-packing problem with bin size constraints might be solvable in polynomial time.…