Maximizing k-Submodular Functions and Beyond

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In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...

We address multi-robot safe mission planning in uncertain dynamic environments. This problem arises in several applications including safety-critical exploration, surveillance, and emergency rescue missions. Computation of a multi-robot optimal control pol ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...

Submodular functions are a widely studied topic in theoretical computer science. They have found several applications both theoretical and practical in the fields of economics, combinatorial optimization and machine learning. More recently, there have also ...

We introduce a new rounding technique designed for online optimization problems, which is related to contention resolution schemes, a technique initially introduced in the context of submodular function maximization. Our rounding technique, which we call o ...

We provide a counterexample to the performance guarantee obtained in the paper "Il'ev, V., Linker, N., 2006. Performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid", which was published in Volume 171 of the Eur ...

This thesis focuses on the maximum matching problem in modern computational settings where the algorithms have to make decisions with partial information. First, we consider two stochastic models called query-commit and price-of-information where the algo ...

An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius rho such that there exist balls of radius rho aro ...

Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. ...

We present a technique for Model Order Reduction (MOR) of frequency-domain problems relying on rational interpolation of vector-valued functions. The selection of the sample points is carried out adaptively according to a greedy procedure. We describe seve ...

We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean multi-player model t ...

Given a source of iid samples of edges of an input graph G with n vertices and m edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in G? Moreover, is it possible to obtain such an estimate in a sm ...

An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius ρ such that there exist balls of radius ρ around ...

The next technological revolution will be interwoven to the proliferation of intelligent systems. As we bridge the gap between physical and cyber worlds, we will give rise to large-scale, multi-agent based technologies. A key challenge that cities of the f ...

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...

The central task in many interactive machine learning systems can be formalized as the sequential optimization of a black-box function. Bayesian optimization (BO) is a powerful model-based framework for \emph{adaptive} experimentation, where the primary go ...

We present new techniques to analyze natural local search algorithms for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given an n-point set X subset of R-d and an integer k, select k points in X so th ...

Vizing's celebrated theorem asserts that any graph of maximum degree Delta admits an edge coloring using at most Delta + 1 colors. In contrast, Bar-Noy, Motwani and Naor showed over a quarter century ago that the trivial greedy algorithm, which uses 2 Delt ...

Knapsack problems give a simple framework for decision making. A classical example is the min-knapsack problem (MinKnap): choose a subset of items with minimum total cost, whose total profit is above a given threshold. While this model successfully general ...

Maximizing k-Submodular Functions and Beyond

Chattez avec Graph Search

Approximation Algorithms for Allocation and Network Design

Multi-robot task allocation for safe planning against stochastic hazard dynamics

Results on Sparse Integer Programming and Geometric Independent Sets

Fairness and Explainability in Clustering Problems

Streaming and Matching Problems with Submodular Functions

Online Contention Resolution Schemes With Applications To Bayesian Selection Problems

A comment on performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid

How to Match in Modern Computational Settings

Fair colorful k-center clustering

A (2+epsilon)-Approximation Algorithm for Preemptive Weighted Flow Time on a Single Machine

MATHICSE Technical Report : Frequency-domain non-intrusive greedy Model Order Reduction based on minimal rational approximation

The One-Way Communication Complexity of Submodular Maximization with Applications to Streaming and Robustness

Space Efficient Approximation to Maximum Matching Size from Uniform Edge Samples

Fair Colorful k-Center Clustering

Efficient Allocations in Constant Time: Towards Scalable Solutions in the Era of Large Scale Intelligent Systems

New Graph Algorithms via Polyhedral Techniques

Robust Adaptive Decision Making: Bayesian Optimization and Beyond

An Improved Analysis of Local Search for Max-Sum Diversification

Tight Bounds for Online Edge Coloring

On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing