Planar p-center problems are solvable in polynomial time when clustering a Pareto Front

平面 Pareto 前沿中 p-分散问题的多项式算法

Polynomial algorithms for p-dispersion problems in a planar Pareto Front

本文研究了从2D Pareto Front中选取代表点的p-分散问题，提出了新变体并利用动态规划为多种变体设计了多项式时间算法。

实例和普遍最优的不精确帕累托前沿界

Instance and Universally Optimal Bounds for Imprecise Pareto Fronts

本文提出了一种在平面中处理重叠区域的算法，该算法在检索次数和运行时间上均达到最优，实现了对不精确帕累托前沿的高效构造。

Preprocessing Imprecise Points for the Pareto Front

In the preprocessing model for uncertain data we are given a set of regions R which model the uncertainty associated with an unknown set of points P. In this model there are two phases: a preprocessing phase, in which we have access only to R, followed by a reconstruction phase, in which we have access to points in P at a certain retrieval cost C per point. We study the following algorithmic question: how fast can we construct the pareto front of P in the preprocessing model? We show that if R is a set of pairwise-disjoint axis-aligned rectangles, then we can preprocess R to reconstruct the Pa…

Faster Distance-Based Representative Skyline and $k$-Center Along Pareto Front in the Plane

We consider the problem of computing the \emph{distance-based representative skyline} in the plane, a problem introduced by Tao, Ding, Lin and Pei [Proc. 25th IEEE International Conference on Data Engineering (ICDE), 2009] and independently considered by Dupin, Nielsen and Talbi [Optimization and Learning - Third International Conference, OLA 2020] in the context of multi-objective optimization. Given a set $P$ of $n$ points in the plane and a parameter $k$, the task is to select $k$ points of the skyline defined by $P$ (also known as Pareto front for $P$) to minimize the maximum distance from…

精确均匀L1间距用于Solow-Polasky多样性在直线和有序Pareto前沿上

Exact Uniform L1 Spacing for Solow-Polasky Diversity on Lines and Ordered Pareto Fronts

本文研究了在一条线上和有序度量集上固定基数的最大化逆矩阵Solow-Polasky多样性，等价于指数核的有限度量幅度。通过已知的有限线间隙公式，证明了对于每个k≥2，[0,1]上唯一的最大化k点子集是等间距的，从而在实线上选择均匀间隙表示。进一步结果将区间定理扩展到有序ℓ1（L1，或曼哈顿）曲线，通过等距转换：最大化集合在累积ℓ1长度上是均匀的。作为结果，单调双目标Pareto前沿允许Solow-Polasky最优有限近似，这些近似在累积目标空间变化上是均匀分布的。示例展示了连续均匀间隙结果如何出现在离散候选集上。