Technology Category
Constraint Satisfaction and Optimization: Other Foundations of Constraint SatisfactionSearch and Optimization: Combinatorial OptimizationKnowledge Representation and Reasoning: Computational Complexity of Reasoning
Bounds for k-centers of point sets under $L_{infty}$-bottleneck distance
🤖 AI Summary
研究在平面上固定大小点集的$k$-中心问题，使用$L_{infty}$瓶颈距离，提供上界和下界，并探讨计算复杂性。
Technology Category
Application Category
📝 Abstract
We consider the $k$-center problem on the space of fixed-size point sets in the plane under the $L_{infty}$-bottleneck distance. While this problem is motivated by persistence diagrams in topological data analysis, we illustrate it as a emph{Restaurant Supply Problem}: given $n$ restaurant chains of $m$ stores each, we want to place supermarket chains, also of $m$ stores each, such that each restaurant chain can select one supermarket chain to supply all its stores, ensuring that each store is matched to a nearby supermarket. How many supermarket chains are required to supply all restaurants? We address this questions under the constraint that any two restaurant chains are close enough under the $L_{infty}$-distance to be satisfied by a single supermarket chain. We provide both upper and lower bounds for this problem and investigate its computational complexity.
Problem
Research questions and friction points this paper is trying to address.
Bounds for k-centers under L∞-bottleneck distance
Restaurant Supply Problem with proximity constraints
Computational complexity of supermarket chain placement
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses L∞-bottleneck distance for k-center problem
Models as Restaurant Supply Problem with constraints
Provides bounds and computational complexity analysis
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