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Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous fractional opti ...
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 ...
In 1948, Claude Shannon laid the foundations of information theory, which grew out of a study to find the ultimate limits of source compression, and of reliable communication. Since then, information theory has proved itself not only as a quest to find the ...
Organocatalysis has evolved significantly over the last decades, becoming a pillar of synthetic chemistry, but traditional theoretical approaches based on quantum mechanical computations to investigate reaction mechanisms and provide rationalizations of ca ...
This study investigated the impact of participating in a year-long digital-fabrication course on high-school seniors' problem-solving skills, with a focus on problems involving mechanistic systems. The research questions centered on whether working in a ma ...
We revisit the problem max-min degree arborescence, which was introduced by Bateni et al. [STOC'09] as a central special case of the general Santa Claus problem, which constitutes a notorious open question in approximation algorithms. In the former problem ...
We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient di ...
We prove an NP upper bound on a theory of integer-indexed integer-valued arrays that extends combi- natory array logic with an ordering relation on the index set and the ability to express sums of elements. We compare our fragment with seven other fragment ...
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 ...