相关论文: The Pareto cover problem

We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…

Consider the Hitting Set problem where, for a given universe $\mathcal{X} = \left\{ 1, ... , n \right\}$ and a collection of subsets $\mathcal{S}_1, ... , \mathcal{S}_m$, one seeks to identify the smallest subset of $\mathcal{X}$ which has…

We introduce and study the computational problem of determining statistical similarity between probability distributions. For distributions $P$ and $Q$ over a finite sample space, their statistical similarity is defined as…

Chv\'{a}tal and Klincsek (1980) gave an $O(n^3)$-time algorithm for the problem of finding a maximum-cardinality convex subset of an arbitrary given set $P$ of $n$ points in the plane. This paper examines a generalization of the problem,…

The uniqueness of an optimal solution to a combinatorial optimization problem attracts many fields of researchers' attention because it has a wide range of applications, it is related to important classes in computational complexity, and an…

In this paper we propose an extension of the Uncapacitated Hub Location Problem where the potential positions of the hubs are not fixed in advance. Instead, they are allowed to belong to a region around an initial discrete set of nodes. We…

Consider the fundamental problem of drawing a simple random sample of size k without replacement from [n] := {1, . . . , n}. Although a number of classical algorithms exist for this problem, we construct algorithms that are even simpler,…

Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$, how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately,…

We consider extension variants of the classical graph problems Vertex Cover and Independent Set. Given a graph $G=(V,E)$ and a vertex set $U \subseteq V$, it is asked if there exists a minimal vertex cover (resp.\ maximal independent set)…

We model equilibrium allocations in a distribution network as the solution of a linear program (LP) which minimizes the cost of unserved demands across nodes in the network. The constraints in the LP dictate that once a given node's supply…

This paper introduces a new type of covering process that covers the set of natural numbers using renewal processes as objects. Inspired by the behavior of prime numbers, the model in each step finds the smallest vacant point, $k$, and…

The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each…

We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…

Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap.…

We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…

In this work, we study the computational complexity of the Minimum Distance Code Detection problem. In this problem, we are given a set of noisy codeword observations and we wish to find a code in a set of linear codes $\mathcal{C}$ of a…

We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…

We study the problem of allocating indivisible items to agents with additive valuations, under the additional constraint that bundles must be connected in an underlying item graph. Previous work has considered the existence and complexity…

In this work we consider the problem of finding the minimum-weight loop cover of an undirected graph. This combinatorial optimization problem is called 2-matching and can be seen as a relaxation of the traveling salesman problem since one…

Risk-sharing is one way to pool risks without the need for a third party. To ensure the attractiveness of such a system, the rule should be accepted and understood by all participants. A desirable risk-sharing rule should fulfill actuarial…