Abstract
We are interested in online graph problems where the knowledge of the underlying graph G (all arriving vertices are from G) has a profound impact on the size of the advice needed to solve the problem efficiently. On one hand, we show that, for sparse graphs, constant-size advice is sufficient to solve the maximum independent set problem with constant competitive ratio, even with no knowledge of the underlying graph. On the other hand, we show a lower bound of Ω(log(n/a)/loglog(n/a)) on the competitive ratio of finding a maximum independent set in bipartite graphs if no knowledge of the underlying graph is available and if the advice is of size a. We complement the lower bounds by providing corresponding upper bounds.
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Dobrev, S., Královič, R., Královič, R. (2013). Independent Set with Advice: The Impact of Graph Knowledge. In: Erlebach, T., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2012. Lecture Notes in Computer Science, vol 7846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38016-7_2
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DOI: https://doi.org/10.1007/978-3-642-38016-7_2
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