Many modern data sources arising from social networks, biological data, etc. are best viewed as indexed by combinatorial structures such as graphs, rather than as time series.

Design of efficient sampling methodologies to capture the information content in sparse, and thus, "compressible" signals is well known as compressive sensing (CS) in the signal processing community.

In a breakthrough, we are able to give a simple description of 'capacity' of cellular wireless networks. Shannon capacity is intractable for most wireless networks, and a surrogate definition is used.

We consider the problem of maintaining a matching and a vertex cover of approximately maximum (resp. minimum) size in a dynamic graph under a sequence of edge insertions and deletions.

Constrained counting and sampling are two fundamental problems in Computer Science with numerous applications, including network reliability, decision making under certainty, probabilistic reasoning, and constrained-random verification.