The second AORC Center-wide monthly seminar is on this Friday (Feb. 23, 2018).
Dinner will be followed after the seminar.
- Time : Feb. 23 (Fri), 2:30 pm - 5:30 pm
- Venue : AORC Seminar Room
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1. 2:30 pm - 3:30 pm : Group 1 presentation & discussion
- Title : (Edge) clique covering number and partition number of graphs and Riordan graphs
- Speaker : Bumtle Kang (SKKU)
- Abstract : Covering and partition of graphs are one of the most interesting topics on graph theory and
they have been widely studied. It has applications to many important problems including representing
intersections of sets by using graphs and many assignment-type problems. In general, it is hard to calculate
because given a graph $G$ and an integer $k$, even deciding whether $G$ has an edge clique cover of size
less than $k$ is NP-complete.
In this talk, we provide a lower bound for edge clique cover number of io-decomposable and ie-decomposable
Riordan graphs, and some more results on Pascal graph. Furthermore, in a connection with edge clique cover
number, we also find out some relations for (vertex) clique cover number and chromatic number in terms of
independent number and matching number.
2. 3:30 pm - 4:30pm : Group 2 presentation & discussion
- Title : Transmission range adjustment with firefly optimization based mobile data collector for wireless sensor networks
- Speaker : Muralitharan Krishnan (SKKU)
- Abstract : In this talk, wireless sensor networks (WSN) clustering with route optimization is to be presented.
The approach involves two steps. First, the cluster head is selected for each sub-region in the WSN. Nest, finding
the optimized route for data collections to increase the network lifetime. Due to limited battery power constraint of sensor nodes, the energy is to be spent appropriately. Data transmission and reception are the major energy consumables in sensor networks. A successful transmission technique plays a big role in increasing the network lifetime.
An algorithm is proposed, to adjust the transmission range according to the distances between the cluster members
and heads. Further, Firefly optimization algorithm-based mobile data collector is employed for data collection to
improve the lifetime of the network.
3. 4:30 pm - 5:30 pm : Group 3 presentation & discussion
- Title : The overpartition function modulo powers of 2
- Speaker : Kyoungmin Kim (SKKU)
- Abstract : Let $\bar{p}(n)$ denote the number of overpartitions of $n$. In $2004$, K. Mahlburg showed
$\bar{p}(n)\equiv 0 \pmod {2^6}$ for a set of integers of arithmetic density $1$ and he conjectured that for all positive integers $k$, $\bar{p}(n)\equiv 0 \pmod {2^k}$ for almost all integers $n$. In this talk, we introduce known results for Mahlburg's conjecture and propose an approach to solve this conjecture.
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