Related papers: Improved approximation algorithm for k-level UFL w…
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…
We study the non-uniform capacitated multi-item lot-sizing (\lotsizing) problem. In this problem, there is a set of demands over a planning horizon of $T$ time periods and all demands must be satisfied on time. We can place an order at the…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
In the past decade, many parameterized algorithms were developed for packing problems. Our goal is to obtain tradeoffs that improve the running times of these algorithms at the cost of computing approximate solutions. Consider a packing…
The facility location problems (FLPs) are a typical class of NP-hard combinatorial optimization problems, which are widely seen in the supply chain and logistics. Many mathematical and heuristic algorithms have been developed for optimizing…
The multi allocation p-hub median problem (MApHM), the multi allocation uncapacitated hub location problem (MAuHLP) and the multi allocation p-hub location problem (MApHLP) are common hub location problems with several practical…
Approximate algorithms for structured prediction problems---such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001)---typically far exceed their theoretical performance guarantees on real-world instances. These…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…
Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most $4$. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts…
Oblivious dimension reduction, \`{a} la the Johnson-Lindenstrauss (JL) Lemma, is a fundamental approach for processing high-dimensional data. We study this approach for Uniform Facility Location (UFL) on a Euclidean input…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE…
We study data clustering problems with $\ell_p$-norm objectives (e.g. $k$-Median and $k$-Means) in the context of individual fairness. The dataset consists of $n$ points, and we want to find $k$ centers such that (a) the objective is…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon…
In the Submodular Facility Location problem (SFL) we are given a collection of $n$ clients and $m$ facilities in a metric space. A feasible solution consists of an assignment of each client to some facility. For each client, one has to pay…