The Densest Subgraph Problem requires us to find, in a given graph, a subset of vertices
whose induced subgraph maximizes a measure of density. The problem has received a …

Graph layout problems are a particular class of combinatorial optimization problems whose
goal is to find a linear layout of an input graph in such way that a certain objective cost is …

Recently, it became apparent that a large number of the most interesting structures and
phenomena of the world can be described by networks. To develop a mathematical theory of …

We consider the following clustering problem: we have a complete graph on n vertices
(items), where each edge (u, v) is labeled either+ or− depending on whether u and v have …

N COMPUTER applications we are used to live with approximation. Var I ious notions of
approximation appear, in fact, in many circumstances. One notable example is the type of …

'Network'is a heavily overloaded term, so that 'network analysis' means different things to
different people. Specific forms of network analysis are used in the study of diverse …

In this paper, we consider the question of determining whether a function f has property P or
is ε-far from any function with property P. A property testing algorithm is given a sample of …

In this paper, we establish max-flow min-cut theorems for several important classes of
multicommodity flow problems. In particular, we show that for any n-node multicommodity …

Finding dense subgraphs is an important graph-mining task with many applications. Given
that the direct optimization of edge density is not meaningful, as even a single edge …

The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-
time) has been shown to be hard to simulate classically, assuming certain complexity …