Superlinear Lower Bounds for Multipass Graph Processing

Superlinear Lower Bounds for Distributed Subgraph Detection

In the distributed subgraph-freeness problem, we are given a graph H , and asked to determine whether the network graph contains H as a subgraph or not. Subgraph-freeness is an extremely local problem: if the network had no bandwidth constraints, we could detect any subgraph H in |H| rounds, by having each node of the network learn its entire |H|-neighborhood. However, when bandwidth is limited...

On Superlinear Lower Bounds in Complexity Theory

This paper first surveys the near-total lack of superlinear lower bounds in complexity theory, for “natural” computational problems with respect to many models of computation. We note that the dividing line between models where such bounds are known and those where none are known comes when the model allows non-local communication with memory at unit cost . We study a model that imposes a “fair...

Superlinear Lower Bounds for Bounded-Width Branching Programs

We use algebraic techniques to obtain superlinear lower bounds on the size of bounded-width branching programs to solve a number of problems. In particular, we show that any bounded-width branching program computing a nonconstant threshold function has length (n log log n); improving on the previous lower bounds known to apply to all such threshold functions. We also show that any program over ...

Some Lower Bounds for Estrada Index

Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given n-vertex graph G can be mapped to the vertices of a given h-vertex graph H such that each edge of G is mapped to an edge of H. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the 2-CSP problem. In this paper, we prove several lower bounds for HOM under the Exponen...