기초과학연구원 이산수학그룹
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Let $G = (V, E)$ be a graph on $n$ vertices, and let $c : E \to P$, where $P$ is a set of colors. Let $\delta^c(G) = \min_{v \in V} \{ d^{c}(v) \}$ where $d^c(v)$ is the number of colors on edges incident to a vertex $v$ of $G$. In 2011, Fujita and Magnant … |
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Flag algebras are a mathematical framework introduced by Alexander Razborov in 2007, which has been used to resolve a wide range of open problems in extremal graph theory in the past twenty years. This framework provides an algebraic setup where one can express relationships between induced subgraph densities symbolically. It also comes with mathematical techniques … |
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In this talk, we show new strongly polynomial work-depth tradeoffs for computing single-source shortest paths (SSSP) in non-negatively weighted directed graphs in parallel. Most importantly, we prove that directed SSSP can be solved within $\widetilde{O}(m+n^{2-\varepsilon})$ work and $\widetilde{O}(n^{1-\varepsilon})$ depth for some positive $\varepsilon>0$. For dense graphs with non-negative real weights, this yields the first nearly … |
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