# Caleb RobelleMassachusetts Institute of Technology | MIT · Computer Science and Artificial Intelligence Laboratory

Bachelor of Science
I am doing research as a PhD student at MIT.

7
Publications
225
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18
Citations
Introduction
Education
June 2017 - May 2021
Field of study
• Mathematics and Computer Science

## Publications

Publications (7)
Preprint
Full-text available
Recent work has established that, for every positive integer $k$, every $n$-node graph has a $(2k-1)$-spanner on $O(f^{1-1/k} n^{1+1/k})$ edges that is resilient to $f$ edge or vertex faults. For vertex faults, this bound is tight. However, the case of edge faults is not as well understood: the best known lower bound for general $k$ is $\Omega(f^{\... Preprint Full-text available Let$k,p\in \mathbb{N}$with$p$prime and let$f\in\mathbb{Z}[x_1,x_2]$be a bivariate polynomial with degree$d$and all coefficients of absolute value at most$p^k$. Suppose also that$f$is variable separated, i.e.,$f=g_1+g_2$for$g_i\in\mathbb{Z}[x_i]$. We give the first algorithm, with complexity sub-linear in$p$, to count the number of ro... Preprint Full-text available Recent work has pinned down the existentially optimal size bounds for vertex fault-tolerant spanners: for any positive integer$k$, every$n$-node graph has a$(2k-1)$-spanner on$O(f^{1-1/k} n^{1+1/k})$edges resilient to$f\$ vertex faults, and there are examples of input graphs on which this bound cannot be improved. However, these proofs work by...
Preprint
Full-text available
It was recently shown that a version of the greedy algorithm gives a construction of fault-tolerant spanners that is size-optimal, at least for vertex faults. However, the algorithm to construct this spanner is not polynomial-time, and the best-known polynomial time algorithm is significantly suboptimal. Designing a polynomial-time algorithm to con...

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