Related papers: Polynomial Time Approximation Schemes for Clusteri…
Clustering of urban traffic patterns is an essential task in many different areas of traffic management and planning. In this paper, two significant applications in the clustering of urban traffic patterns are described. The first…
The problem of routing in graphs using node-disjoint paths has received a lot of attention and a polylogarithmic approximation algorithm with constant congestion is known for undirected graphs [Chuzhoy and Li 2016] and [Chekuri and Ene…
Projective clustering is a problem with both theoretical and practical importance and has received a great deal of attentions in recent years. Given a set of points $P$ in $\mathbb{R}^{d}$ space, projective clustering is to find a set…
Pruhs and Woeginger prove the existence of FPTAS's for a general class of minimization and maximization subset selection problems. Without losing generality from the original framework, we prove how better asymptotic worst-case running…
We study the classic \textsc{(Uncapacitated) Facility Location} problem on Unit Disk Graphs (UDGs). For a given point set $P$ in the plane, the unit disk graph UDG(P) on $P$ has vertex set $P$ and an edge between two distinct points $p, q…
In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge…
We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time…
We investigate the classic Knapsack problem and propose a fully polynomial-time approximation scheme (FPTAS) that runs in $\widetilde{O}(n + (1/\varepsilon)^2)$ time. This improves upon the $\widetilde{O}(n + (1/\varepsilon)^{11/5})$-time…
We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…
Hard-capacitated $k$-means (HCKM) is one of the fundamental problems remaining open in combinatorial optimization and data mining areas. In this problem, one is required to partition a given $n$-point set into $k$ disjoint clusters with…
A classical branch of graph algorithms is graph transversals, where one seeks a minimum-weight subset of nodes in a node-weighted graph $G$ which intersects all copies of subgraphs~$F$ from a fixed family $\mathcal F$. Many such graph…
A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…
We describe a distributed randomized algorithm computing approximate distances and routes that approximate shortest paths. Let n denote the number of nodes in the graph, and let HD denote the hop diameter of the graph, i.e., the diameter of…
For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least…
The k-Clique problem is a canonical hard problem in parameterized complexity. In this paper, we study the parameterized complexity of approximating the k-Clique problem where an integer k and a graph G on n vertices are given as input, and…
We present a unified polynomial-time approximation scheme (PTAS) for the prize collecting traveling salesman problem (PCTSP) and the prize collecting Steiner tree problem (PCSTP) in doubling metrics. Given a metric space and a penalty…
We consider the problem of computing compact routing tables for a (weighted) planar graph $G:= (V, E,w)$ in the PRAM, CONGEST, and the novel HYBRID communication model. We present algorithms with polylogarithmic work and communication that…
We consider the classical scheduling problem on parallel identical machines to minimize the makespan, and achieve the following results under the Exponential Time Hypothesis (ETH) 1. The scheduling problem on a constant number $m$ of…
This paper derives polynomial-time approximation schemes for several NP-hard stochastic optimization problems from the algorithmic mechanism design and operations research literatures. The problems we consider involve a principal or seller…
Traffic state data, such as speed, volume and travel time collected from ubiquitous traffic monitoring sensors require advanced network level analytics for forecasting and identifying significant traffic patterns. This paper leverages…