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We show that a constant factor approximation of the shortest and closest lattice vector problem in any l(p)-norm can be computed in time 2((0.802 + epsilon)n). This matches the currently fastest constant factor approximation algorithm for the shortest vect ...
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 p ...
This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theor ...
We consider the problem of solving integer programs of the form min {c^⊺ x : Ax = b, x ∈ ℤ_{⩾ 0}}, where A is a multistage stochastic matrix in the following sense: the primal treedepth of A is bounded by a parameter d, which means that the columns of A ca ...
Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021
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 ...
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 ...
Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...
This thesis focuses on designing spectral tools for graph clustering in sublinear time. With the emergence of big data, many traditional polynomial time, and even linear time algorithms have become prohibitively expensive. Processing modern datasets requir ...
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 ...
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. The input consists of a set of jobs, characterized by their processing times, release time ...
