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Linda Cook, A tight algorithmic meta-theorem for distributed certification within bounded treewidth graphs
July 22 Tuesday @ 4:30 PM - 5:30 PM KST
A local certification of a graph property is a protocol in which nodes are given “certificates of a graph property” that allow the nodes to check whether their network has this property while only communicating with their local network. The key property of a local certification is that if certificates are corrupted, some node in the network will be able to recognize this. Inspired by practical concerns, the aim in LOCAL certification is to minimize the maximum size of a certificate.
In this talk we introduce local certification and open problems in the area and present some recent joint work with Eunjung Kim and Tomáš Masařík, A Tight Meta-theorem for LOCAL Certification of MSO2 Properties within Bounded Treewidth Graphs.
In this work, instead of considering a specific graph property and developing a local certification protocol tailor-made for this property, we aim for generic protocols that can certify any property expressible in a certain logical framework. We consider Monadic Second Order Logic (MSO