Dependent rounding and its applications to approximation algorithms

We develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include: -low congestion multi-path routing; -richer random-graph models for graphs with a given degree-sequence; -improved approximation algorithms for: (i) throughput-maximization in broadcast scheduling, (ii) delay-minimization in broadcast scheduling, as well as (iii) capacitated vertex cover; and -fair scheduling of jobs on unrelated parallel machines.