44 citations · 71 across the 21 of their papers we have counts for
24 papers
Network Routing on Regular Digraphs and Their Line Graphs
Vance Faber, Noah Streib
This paper concerns all-to-all network routing on regular digraphs. In previous work we focused on efficient routing in highly symmetric digraphs with low diameter for fixed degree…
Existence of a Moore graph of degree 57 is still open
Vance Faber, Jonathan Keegan
In 2020, a paper [arXiv:2010.13443] appeared in the arXiv claiming to prove that a Moore graph of diameter 2 and degree 57 does not exist. (The paper is in Russian; we include a li…
On the Forsythe conjecture
Vance Faber, Jörg Liesen, Petr Tichý
Forsythe formulated a conjecture about the asymptotic behavior of the restarted conjugate gradient method in 1968. We translate several of his results into modern terms, and genera…
All-to-all Routing on Digraph Networks
Nyumbu Chishwashwa, Vance Faber, Noah Streib
We discuss an open problem and its converse first posed by Dougherty and Faber in [3], "Network routing on regular directed graphs from spanning factorizations." Does every vertex…
Which Cubic Graphs have Quadrangulated Spherical Immersions?
Lowell Abrams, Yosef Berman, Vance Faber +1
We consider spherical quadrangulations -- spherical embeddings of multigraphs, possibly with loops, so that every face has boundary walk of length 4 -- in which all vertices have d…
Bounds and algorithms for graph trusses
Paul Burkhardt, Vance Faber, David G. Harris
The -truss, introduced by Cohen (2005), is a graph where every edge is incident to at least triangles. This is a relaxation of the clique. It has proved to be a useful tool…
Edge-coloring linear hypergraphs with medium-sized edges
Vance Faber, David G. Harris
Motivated by the Erdős-Faber-Lovász (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We show that if the hyper-edge sizes are bounded bet…
Linear Hypergraph List Edge Coloring - Generalizations of the EFL Conjecture to List Coloring
Vance Faber
Motivated by the Erdős-Faber-Lovász (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We discuss several conjectures for list edge colorin…
Tight bounds and conjectures for the isolation lemma
Vance Faber, David G. Harris
Given a hypergraph and a weight function on its vertices, we say that is isolating if there is exactly one edge of minimum weight $w(e) =…
Linear Hypergraph Edge Coloring
Vance Faber
Motivated by the Erdos-Faber Lovasz conjecture (EFL) for hypergraphs, we explore relationships between several conjectures on the edge coloring of linear hypergraphs. In particular…
Hypergraph Versals
Vance Faber, Noah Streib
Let H be a hypergraph on n vertices with the property that no edge contains another. We prove some results for a special case of the Isolation Lemma when the label set for the edge…
Transpose on vertex symmetric digraphs
Vance Faber
We discuss transpose (sometimes called universal exchange or all-to-all) on vertex symmetric networks. We provide a method to compare the efficiency of transpose schemes on two dif…
Network routing on regular directed graphs from spanning factorizations
Randall Dougherty, Vance Faber
Networks with a high degree of symmetry are useful models for parallel processor networks. In earlier papers, we defined several global communication tasks (universal exchange, uni…
Automorphisms of the cycle prefix digraph
William Y. C. Chen, Vance Faber, Bingqing Li
Cycle prefix digraphs have been proposed as an efficient model of symmetric interconnection networks for parallel architecture. It has been discovered that the cycle prefix network…
Analysis of first order systems for the solution of Laplace's equation
Vance Faber
Kelner, Orecchia, Sidford, and Zhu have given a randomized iterative method for approximating the solution to the discrete Laplace equation that has expected running time nearly li…
Global communication algorithms for Cayley graphs
Vance Faber
We discuss several combinatorial problems that arise when one looks at computational algorithms for highly symmetric networks of processors. More specifically, we are interested in…
Characterization of worst-case GMRES
Vance Faber, Jörg Liesen, Petr Tichý
Given a matrix and iteration step , we study a best possible attainable upper bound on the GMRES residual norm that does not depend on the initial vector . This quantity…
Livelock free routing schemes
Vance Faber
We give a livelock free routing algorithm for any allowed network. Unlike some other solutions to this problem: 1) packets entering the network have an absolute upper bound on the…
Global sum on symmetric networks
Vance Faber
We are interested in the following problem we call global sum. Each processor starts with a single real value. At each time step, every directed edge in the graph can simultaneousl…
A Problem of W. R. Scott: Classify the Subgroup of Elements with Many Roots
Vance Faber
Let G be an infinite group and let h and g be elements. We say that h is a root of g if some integer power of h is equal to g. We define K(G) to be the subgroup of all elements of…
Algebraic constructions of efficient broadcast networks
Michael J. Dinneen, Vance Faber, Michael R. Fellows
Cayley graph techniques are introduced for the problem of constructing networks having the maximum possible number of nodes, among networks that satisfy prescribed bounds on the pa…
The degree-diameter problem for several varieties of Cayley graphs, I: the Abelian case
Randall Dougherty, Vance Faber
We address the degree-diameter problem for Cayley graphs of Abelian groups (Abelian graphs), both directed and undirected. The problem turns out to be closely related to the proble…
Restricted routing and wide diameter of the cycle prefix network
William Y. C. Chen, Vance Faber, Emanuel Knill
The cycle prefix network is a Cayley coset digraph based on sequences over an alphabet which has been proposed as a vertex symmetric communication network. This network has been sh…
Inverting sets and the packing problem
Vance Faber, Mark Goldberg, Emanuel Knill +1
Given a set , a subset , and a permutation of , we say that permutes if . Given a collection $\cS = \{V; S_1,\ldots , S_m\}$, where $S…