Fast distributed graph partition and application

This paper presents efficient deterministic and randomized distributed algorithms for decomposing a graph with n nodes into a disjoint set of connected clusters with small radius and few intercluster edges. Our algorithms can be easily implemented in the distributed CONGEST model of computation i.e., limited message size, improving the time complexity of previous algorithms (Moran and Snir, 2000; Awerbuch, 1985; Peleg, 2000) from linear to sublinear. One important application of our algorithms is efficient construction of sparse graph spanners. In fact, given a parameter k, we show that there exists a sublinear deterministic distributed algorithm that constructs a graph spanner of stretch 2k - 1 with at most O(n
¹⁺¹
k/) edges in the CONGEST model