Michael Zlatin
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View article: The Online Submodular Assignment Problem
The Online Submodular Assignment Problem Open
Online resource allocation is a rich and varied field. One of the most well-known problems in this area is online bipartite matching, introduced in 1990 by Karp, Vazirani, and Vazirani [KVV90]. Since then, many variants have been studied, …
View article: The Online Submodular Assignment Problem
The Online Submodular Assignment Problem Open
Online resource allocation is a rich and varied field. One of the most well-known problems in this area is online bipartite matching, introduced in 1990 by Karp, Vazirani, and Vazirani [KVV90]. Since then, many variants have been studied, …
View article: Approximation Algorithms for Steiner Connectivity Augmentation
Approximation Algorithms for Steiner Connectivity Augmentation Open
We consider connectivity augmentation problems in the Steiner setting, where the goal is to augment the edge-connectivity between a specified subset of terminal nodes. In the Steiner Augmentation of a Graph problem (k-SAG), we are given a …
View article: On small-depth tree augmentations
On small-depth tree augmentations Open
We study the Weighted Tree Augmentation Problem for general link costs. We show that the integrality gap of the odd-LP relaxation for the (weighted) Tree Augmentation Problem for a k-level tree instance is at most 2−12k−1. For 2- and 3-lev…
View article: Approximation algorithms for Steiner Tree Augmentation Problems
Approximation algorithms for Steiner Tree Augmentation Problems Open
In the Steiner Tree Augmentation Problem (STAP), we are given a graph $G = (V,E)$, a set of terminals $R \subseteq V$, and a Steiner tree $T$ spanning $R$. The edges $L := E \setminus E(T)$ are called links and have non-negative costs. The…
View article: On packing dijoins in digraphs and weighted digraphs
On packing dijoins in digraphs and weighted digraphs Open
Let $D=(V,A)$ be a digraph. A dicut is a cut $δ^+(U)\subseteq A$ for some nonempty proper vertex subset $U$ such that $δ^-(U)=\emptyset$, a dijoin is an arc subset that intersects every dicut at least once, and more generally a $k$-dijoin …
View article: On Small-Depth Tree Augmentations
On Small-Depth Tree Augmentations Open
We study the Weighted Tree Augmentation Problem for general link costs. We show that the integrality gap of the ODD-LP relaxation for the (weighted) Tree Augmentation Problem for a $k$-level tree instance is at most $2 - \frac{1}{2^{k-1}}$…
View article: Unique Rectification in $d$-Complete Posets: Towards the $K$-Theory of Kac-Moody Flag Varieties
Unique Rectification in $d$-Complete Posets: Towards the $K$-Theory of Kac-Moody Flag Varieties Open
The jeu-de-taquin-based Littlewood-Richardson rule of H. Thomas and A. Yong (2009) for minuscule varieties has been extended in two orthogonal directions, either enriching the cohomology theory or else expanding the family of varieties con…
View article: Unique rectification in $d$-complete posets: towards the $K$-theory of\n Kac-Moody flag varieties
Unique rectification in $d$-complete posets: towards the $K$-theory of\n Kac-Moody flag varieties Open
The jeu-de-taquin-based Littlewood-Richardson rule of H. Thomas and A. Yong\n(2009) for minuscule varieties has been extended in two orthogonal directions,\neither enriching the cohomology theory or else expanding the family of\nvarieties …