Estimating Graph Parameters from Random Order Streams

We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with probability at least 2/3, • the number of connected components of G can be approximated up to an additive error of εn using (1ε ) O(1/ε) space, • the weight of a minimum spanning tree of a connected input graph with integer edges weights from {1, . . . ,W} can be approximated within a multiplicative factor of 1+ ε using ( 1 ε )Õ(W /ε) space, • the size of a maximum independent set in planar graphs can be approximated within a multiplicative factor of 1 + ε using space 2 (1/ε)log O(1)(1/ε) . Faculty of Computer Science, University of Vienna, Austria. Email: [email protected]. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement no. 340506. Department of Computer Science, TU Dortmund, Germany. Email: [email protected]. Supported by ERC Starting Grant 307696.