Space Efficient Algorithms for Some Graph Theoretical Problems

Joseph F. JáJá, Janos Simon

Abstract: We present space-efficient-O(log2 n)-deterministic algorithms for some graph theoretical problems such as planarity testing, producing a plane embedding, finding minimum cost spanning trees, obtaining the connected, biconnected and triconnected components of a graph. Previous planarity algorithms used Ω(n) space. Several algorithms are based on a space-efficient matrix inversion method. The same bounds hold for uniform circuit depth.