7 research outputs found
Families of Small Regular Graphs of Girth 5
In this paper we obtain --regular graphs of girth 5 with fewer
vertices than previously known ones for and for any prime performing operations of reductions and amalgams on the Levi graph of
an elliptic semiplane of type . We also obtain a 13-regular graph of
girth 5 on 236 vertices from using the same technique
Optimizing the Transition Waste in Coded Elastic Computing
Distributed computing, in which a resource-intensive task is divided into
subtasks and distributed among different machines, plays a key role in solving
large-scale problems, e.g., machine learning for large datasets or massive
computational problems arising in genomic research. Coded computing is a
recently emerging paradigm where redundancy for distributed computing is
introduced to alleviate the impact of slow machines, or stragglers, on the
completion time. Motivated by recently available services in the cloud
computing industry, e.g., EC2 Spot or Azure Batch, where spare/low-priority
virtual machines are offered at a fraction of the price of the on-demand
instances but can be preempted in a short notice, we investigate coded
computing solutions over elastic resources, where the set of available machines
may change in the middle of the computation. Our contributions are two-fold: We
first propose an efficient method to minimize the transition waste, a newly
introduced concept quantifying the total number of tasks that existing machines
have to abandon or take on anew when a machine joins or leaves, for the cyclic
elastic task allocation scheme recently proposed in the literature (Yang et al.
ISIT'19). We then proceed to generalize such a scheme and introduce new task
allocation schemes based on finite geometry that achieve zero transition wastes
as long as the number of active machines varies within a fixed range. The
proposed solutions can be applied on top of every existing coded computing
scheme tolerating stragglers.Comment: 16 page
Tactical (de-)compositions of symmetric configurations
We introduce a new method to describe tactical (de-)compositions of symmetric configurations via block (0,1)-matrices with constant row and column sum having circulant blocks. This method allows us to prove the existence of an infinite class of symmetric configurations of type where p is any prime and s≤t is a positive integer such that t−1 is the greatest prime power with . In particular, we obtain a new configuration