On Graph Problems in a Semi-streaming Model

Massive graphs arise naturally in a lot of applications, especially in communication networks like the internet. The size of these graphs makes it very hard or even impossible to store set of edges in the main memory. Thus, random access to the edges can't be realized, which makes most o ine algorithms unusable. This essay investigates e cient algorithms that read the edges only in a xed sequential order. Since even basic graph problems often need at least linear space in the number of vetices to be solved, the storage space bounds are relaxed compared to the classic streaming model, such that the bound is O(n · polylog n). The essay describes algorithms for approximations of the unweighted and weighted matching problem and gives a o(log1− n) lower bound for approximations of the diameter. Finally, some results for further graph problems are discussed.