Related papers: A Tree Structure For Dynamic Facility Location
In the facility location problem, the task is to place one or more facilities so as to minimize the sum of the agent costs for accessing their nearest facility. Heretofore, in the strategic version, agent locations have been assumed to be…
Recent years have witnessed the rise of many successful e-commerce marketplace platforms like the Amazon marketplace, AirBnB, Uber/Lyft, and Upwork, where a central platform mediates economic transactions between buyers and sellers.…
We consider a multi-stage facility reallocation problems on the real line, where a facility is being moved between time stages based on the locations reported by $n$ agents. The aim of the reallocation algorithm is to minimise the social…
We propose a dynamic data structure for the distribution-sensitive point location problem. Suppose that there is a fixed query distribution in $\mathbb{R}^2$, and we are given an oracle that can return in $O(1)$ time the probability of a…
We consider the numerical taxonomy problem of fitting a positive distance function ${D:{S\choose 2}\rightarrow \mathbb R_{>0}}$ by a tree metric. We want a tree $T$ with positive edge weights and including $S$ among the vertices so that…
Mobile micro-clouds are promising for enabling performance-critical cloud applications. However, one challenge therein is the dynamics at the network edge. In this paper, we study how to place service instances to cope with these dynamics,…
In this paper we consider methods for dynamically storing a set of different objects ("modules") in a physical array. Each module requires one free contiguous subinterval in order to be placed. Items are inserted or removed, resulting in a…
The Maximal Covering Location Problem (MCLP) represents a fundamental optimization challenge in facility location theory, where the objective is to maximize demand coverage while operating under resource constraints. This paper presents a…
We introduce an online variant of mobile facility location (MFL) (introduced by Demaine et al. [SODA' 07]). We call this new problem online mobile facility location (OMFL). In the OMFL problem, initially, we are given a set of $k$ mobile…
Temporal graphs represent interactions between entities over time. Deciding whether entities can reach each other through temporal paths is useful for various applications such as in communication networks and epidemiology. Previous works…
We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…
In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…
In traditional facility location problems, a set of points is provided, and the objective is to determine the best location for a new facility based on criteria such as minimizing cost, time, and distances between clients and facilities.…
The facility location problem is a well-known challenge in logistics that is proven to be NP-hard. In this paper we specifically simulate the geographical placement of facilities to provide adequate service to customers. Determining…
We study the online metric matching problem. There are $m$ servers and $n$ requests located in a metric space, where all servers are available upfront and requests arrive one at a time. Upon the arrival of a new request, it needs to be…
We consider the classic Facility Location, $k$-Median, and $k$-Means problems in metric spaces of doubling dimension $d$. We give nearly linear-time approximation schemes for each problem. The complexity of our algorithms is…
We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…
A tree-packing is a collection of spanning trees of a graph. It has been a useful tool for computing the minimum cut in static, dynamic, and distributed settings. In particular, [Thorup, Comb. 2007] used them to obtain his dynamic min-cut…
The classic online facility location problem deals with finding the optimal set of facilities in an online fashion when demand requests arrive one at a time and facilities need to be opened to service these requests. In this work, we study…
A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treats…