Daniel Hathcock
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View article: Perfect Fractional Matchings in Bipartite Graphs Via Proportional Allocations
Perfect Fractional Matchings in Bipartite Graphs Via Proportional Allocations Open
Given a bipartite graph that has a perfect matching, a prefect proportional allocation is an assignment of positive weights to the nodes of the right partition so that every left node is fractionally assigned to its neighbors in proportion…
View article: The Steiner path aggregation problem
The Steiner path aggregation problem Open
In the Steiner Path Aggregation Problem, our goal is to aggregate paths in a directed network into a single arborescence without significantly disrupting the paths. In particular, we are given a directed multigraph with colored arcs, a roo…
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: Maintaining Matroid Intersections Online
Maintaining Matroid Intersections Online Open
Maintaining a maximum bipartite matching online while minimizing recourse/augmentations is a well studied problem, motivated by content delivery, job scheduling, and hashing. A breakthrough result of Bernstein, Holm, and Rotenberg (\emph{S…
View article: One Tree to Rule Them All: Poly-Logarithmic Universal Steiner Tree
One Tree to Rule Them All: Poly-Logarithmic Universal Steiner Tree Open
A spanning tree $T$ of graph $G$ is a $ρ$-approximate universal Steiner tree (UST) for root vertex $r$ if, for any subset of vertices $S$ containing $r$, the cost of the minimal subgraph of $T$ connecting $S$ is within a $ρ$ factor of the …
View article: Toppleable permutations, excedances and acyclic orientations
Toppleable permutations, excedances and acyclic orientations Open
Recall that an excedance of a permutation $\pi$ is any position $i$ such that $\pi_i > i$. Inspired by the work of Hopkins, McConville and Propp (Elec. J. Comb., 2017) on sorting using toppling, we say that a permutation is toppleable if i…
View article: Toppleable Permutations, Excedances and Acyclic Orientations
Toppleable Permutations, Excedances and Acyclic Orientations Open
Recall that an excedance of a permutation $π$ is any position $i$ such that $π_i > i$. Inspired by the work of Hopkins, McConville and Propp (Elec. J. Comb., 2017) on sorting using toppling, we say that a permutation is toppleable if it ge…
View article: On the hypergraph connectivity of skeleta of polytopes
On the hypergraph connectivity of skeleta of polytopes Open
We show that for every $d$-dimensional polytope, the hypergraph whose nodes are $k$-faces and whose hyperedges are $(k+1)$-faces of the polytope is strongly $(d-k)$-vertex connected, for each $0 \leq k \leq d- 1$.