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On the Integrality Gap of Binary Integer Programs with Gaussian Data
TLDR
The results give a Gaussian analogue of the classical integrality gap result of Dyer and Frieze in the case of random packing IPs and proves that the gap between the value of the linear programming relaxation and the IP is upper bounded by $\operatorname{poly}(m)(\log n)^2 / n$.
New FPT algorithms for finding the temporal hybridization number for sets of phylogenetic trees
TLDR
An algorithm for computing a tree-child network with temporal distance at most d and at most k reticulations in the jats:inline-formula, and the concept of <jats:italic>temporal distance, which is a measure for how close a tree -child network is to being temporal.
Majorizing Measures for the Optimizer
TLDR
An algorithmic proof of the majorizing measures theorem is given based on the simple observation that finding the best majorizing measure can be cast as a convex program, which allows for efficiently computing the measure using off-the-shelf methods from convex optimization.
A multidimensional solution to additive homological equations
In this paper we prove that for a finite-dimensional real normed space V , every bounded mean zero function f ∈ L∞([0, 1];V ) can be written in the form f = g◦T−g for some g ∈ L∞([0, 1];V ) and some
Integrality Gaps for Random Integer Programs via Discrepancy
We give bounds on the additive gap between the value of a random integer program maxcTx,Ax≤ b,x ∈ {0,1}n with m constraints and that of its linear programming relaxation for a range of distributions
Using the slice rank for finding upper bounds on the size of cap sets
The cap set problem consists of finding the maximum size cap sets, i.e. sets without a 3-term arithmetic progression in F₃. In this thesis several known results on the behavior of this number as n →