Related papers: The Subset Assignment Problem for Data Placement i…
In this paper, we study the Dynamic Parameterized Subset Sampling (DPSS) problem in the Word RAM model. In DPSS, the input is a set,~$S$, of~$n$ items, where each item,~$x$, has a non-negative integer weight,~$w(x)$. Given a pair of query…
The \Problem{knapsack} problem is a fundamental problem in combinatorial optimization. It has been studied extensively from theoretical as well as practical perspectives as it is one of the most well-known NP-hard problems. The goal is to…
Inconsistent values are commonly encountered in real-world applications, which can negatively impact data analysis and decision-making. While existing research primarily focuses on identifying the smallest removal set to resolve…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
Bin Packing with $k$ bins is a fundamental optimisation problem in which we are given a set of $n$ integers and a capacity $T$ and the goal is to partition the set into $k$ subsets, each of total sum at most $T$. Bin Packing is NP-hard…
The goal of data-driven algorithm design is to obtain high-performing algorithms for specific application domains using machine learning and data. Across many fields in AI, science, and engineering, practitioners will often fix a family of…
In the incremental knapsack problem ($\IK$), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of $T$ periods and the capacity of the knapsack is $B_t$ in period $t$ for $t = 1, \ldots, T$.…
Assigning jobs onto identical machines with the objective to minimize the maximal load is one of the most basic problems in combinatorial optimization. Motivated by product planing and data placement, we study a natural extension called…
This paper considers a hierarchical caching system where a server connects with multiple mirror sites, each connecting with a distinct set of users, and both the mirror sites and users are equipped with caching memories. Although there…
Next-generation mobile networks are expected to facilitate fast AI model downloading to end users. By caching models on edge servers, mobile networks can deliver models to end users with low latency, resulting in a paradigm called edge…
The paper addresses problem of data allocation in two-layer computer storage while taking into account dynamic digraph(s) over computing tasks. The basic version of data file allocation on parallel hard magnetic disks is considered as…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
The structure of many real-world optimization problems includes minimization of a nonlinear (or quadratic) functional subject to bound and singly linear constraints (in the form of either equality or bilateral inequality) which are commonly…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
We study a clustering problem where the goal is to maximize the coverage of the input points by $k$ chosen centers. Specifically, given a set of $n$ points $P \subseteq \mathbb{R}^d$, the goal is to pick $k$ centers $C \subseteq…
Traditionally, clustering algorithms focus on partitioning the data into groups of similar instances. The similarity objective, however, is not sufficient in applications where a fair-representation of the groups in terms of protected…
Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on…
The study of {\em balls-into-bins processes} or {\em occupancy problems} has a long history. These processes can be used to translate realistic problems into mathematical ones in a natural way. In general, the goal of a balls-into-bins…
A new scheme for the problem of centralized coded caching with non-uniform demands is proposed. The distinguishing feature of the proposed placement strategy is that it admits equal sub-packetization for all files while allowing the users…
The Bin Packing Problem is one of the most important problems in discrete optimization, as it captures the requirements of many real-world problems. Because of its importance, it has been approached with the main theoretical and practical…