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Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
The tie-line scheduling problem in a multi-area power system seeks to optimize tie-line power flows across areas that are independently operated by different system operators (SOs). In this paper, we leverage the theory of multi-parametric…
This paper provides three nearly-optimal algorithms for scheduling $t$ jobs in the $\mathsf{CLIQUE}$ model. First, we present a deterministic scheduling algorithm that runs in $O(\mathsf{GlobalCongestion} + \mathsf{dilation})$ rounds for…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
Submodular functions are a special class of set functions which naturally model the notion of representativeness, diversity, coverage etc. and have been shown to be computationally very efficient. A lot of past work has applied submodular…
The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal. When this algorithm…
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…
Consider the classical Min-Sum Set Cover problem: We are given a universe $\mathcal{U}$ of $n$ elements and a collection $\mathcal{S}$ of $k$ subsets of $\mathcal{U}$. Moreover, a cost function is associated with each set. The goal is to…
This paper introduces an integrated lot sizing and scheduling problem inspired from a real-world application in off-the-road tire industry. This problem considers the assignment of different items on parallel machines with complex…
The manpower scheduling problem is a kind of critical combinational optimization problem. Researching solutions to scheduling problems can improve the efficiency of companies, hospitals, and other work units. This paper proposes a new model…
Optimistic parallelization is a promising approach for the parallelization of irregular algorithms: potentially interfering tasks are launched dynamically, and the runtime system detects conflicts between concurrent activities, aborting and…
Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…
The operating system's role in a computer system is to manage the various resources. One of these resources is the Central Processing Unit. It is managed by a component of the operating system called the CPU scheduler. Schedulers are…
Optimization problems often involve vector norms, which has led to extensive research on developing algorithms that can handle objectives beyond the $\ell_p$ norms. Our work introduces the concept of submodular norms, which are a versatile…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
Many sequential decision making problems can be formulated as an adaptive submodular maximization problem. However, most of existing studies in this field focus on pool-based setting, where one can pick items in any order, and there have…
The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…
Scheduling jobs with given processing times on identical parallel machines so as to minimize their total completion time is one of the most basic scheduling problems. We study interesting generalizations of this classical problem involving…
Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…