21 citations · 39 across the 9 of their papers we have counts for
9 papers
PolarStar: Expanding the Scalability Horizon of Diameter-3 Networks
Kartik Lakhotia, Laura Monroe, Kelly Isham +4
We present PolarStar, a novel family of diameter-3 network topologies derived from the star product of low-diameter factor graphs. PolarStar gives the largest known diameter-3 netw…
PolarFly: A Cost-Effective and Flexible Low-Diameter Topology
Kartik Lakhotia, Maciej Besta, Laura Monroe +4
In this paper we present PolarFly, a diameter-2 network topology based on the Erdos-Renyi family of polarity graphs from finite geometry. This is a highly scalable low-diameter top…
Takagi Function Identities on Dyadic Rationals
Laura Monroe
The number of unbalanced interior nodes of divide-and-conquer trees on leaves is known to form a sequence of dilations of the Takagi function on dyadic rationals. We use this f…
Binary Signed-Digit Integers and the Stern Polynomial
Laura Monroe
The binary signed-digit representation of integers is used for efficient computation in various settings. The Stern polynomial is a polynomial extension of the well-studied Stern d…
A Class of Trees Having Near-Best Balance
Laura Monroe
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND g…
Binary Signed-Digit Integers and the Stern Diatomic Sequence
Laura Monroe
Stern's diatomic sequence is a well-studied and simply defined sequence with many fascinating characteristics. The binary signed-digit representation of integers is an alternative…
Binary Signed-Digit Integers, the Stern Diatomic Sequence and Stern Polynomials
Laura Monroe
Stern's diatomic sequence is a well-studied and simply defined sequence with many fascinating characteristics. The binary signed-digit (BSD) representation of integers is used wide…
Arithmetic of idempotents in
Kelly Isham, Laura Monroe
Idempotent elements are a well-studied part of ring theory, with several identities of the idempotents in already known. Although the idempotents are not c…
On structures induced by the power sequences of \mathbb{Z}/ m\mathbb{Z}
Kelly Isham, Laura Monroe
In this paper, we explore the structure of in terms of its orbits under modular exponentiation, illustrating this with a sequential power graph that is na…