Abstract
We study random instances of a general graph partitioning problem: the vertex set of the random input graph G consists of k classes V 1,...,V k , and V i -V j -edges are present with probabilities p ij independently. The main result is that with high probability a partition S 1,...,S k of G that coincides with V 1,...,V k on a huge subgraph core(G) can be computed in polynomial time via spectral techniques. The result covers the case of sparse graphs (average degree O(1)) as well as the massive case (average degree #V(G)–O(1)). Furthermore, the spectral algorithm is adaptive in the sense that it does not require any information about the desired partition beyond the number k of classes.
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Coja-Oghlan, A. (2006). An Adaptive Spectral Heuristic for Partitioning Random Graphs. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_60
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DOI: https://doi.org/10.1007/11786986_60
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