Related papers: Multiway Cuts with a Choice of Representatives
Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
The cable-trench problem is defined as a linear combination of the shortest path and the minimum spanning tree problem. In particular, the goal is to find a spanning tree that simultaneously minimizes its total length and the total path…
Selecting a small set of representatives from a large database is important in many applications such as multi-criteria decision making, web search, and recommendation. The $k$-regret minimizing set ($k$-RMS) problem was recently proposed…
We give an improved branch-and-bound solver for the multiterminal cut problem, based on the recent work of Henzinger et al.. We contribute new, highly effective data reduction rules to transform the graph into a smaller equivalent instance.…
Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…
A restriction in the quality and quantity of available qubits presents a substantial obstacle to the application of near-term and early fault-tolerant quantum computers in practical tasks. To confront this challenge, some techniques for…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
We propose a procedure to build a decision tree which approximates the performance of complex machine learning models. This single approximation tree can be used to interpret and simplify the predicting pattern of random forests (RFs) and…
Purpose: Multiwinner voting rules typically require full knowledge of voter preferences, which becomes impractical in large-scale or attention-limited settings. This paper investigates how accurately a winning committee can be approximated…
We study strategic candidate positioning in multidimensional spatial-voting elections. Voters and candidates are represented as points in $\mathbb{R}^d$, and each voter supports the candidate that is closest under a distance induced by an…
We propose a new method for identifying cutting locations for quantum circuit cutting, with a primary focus on partitioning circuits into three or more parts. Under the assumption that the classical postprocessing function is decomposable,…
We consider the online $k$-taxi problem, a generalization of the $k$-server problem, in which $k$ taxis serve a sequence of requests in a metric space. A request consists of two points $s$ and $t$, representing a passenger that wants to be…
We introduce a variant of Multicut Decomposition Algorithms (MuDA), called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates strategies to select the most…
Given a graph $G = (V,E)$ and a terminal $s\in V$, a cut $X$ for $s$ is a vertex set that contains $s$. We look for a cut that is small in two senses, i.e., there are no more than $k$ vertices in $X$ and no more than $t$ edges leaving $X$.…
In this paper, we study a \emph{multicut-mimicking network} for a hypergraph over terminals $T$ with a parameter $c$. It is a hypergraph preserving the minimum multicut values of any set of pairs over $T$ where the value is at most $c$.…
In this paper, we study the problem of approximating the minimum cut in a distributed message-passing model, the CONGEST model. The minimum cut problem has been well-studied in the context of centralized algorithms. However, there were no…
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) $n$-vertex graph $G$ along with $k$ terminal pairs…
Super-resolution (SR) networks have been investigated for a while, with their mobile and lightweight versions gaining noticeable popularity recently. Quantization, the procedure of decreasing the precision of network parameters (mostly FP32…
We consider the problem of assigning weights to a set of samples or data records, with the goal of achieving a representative weighting, which happens when certain sample averages of the data are close to prescribed values. We frame the…