We show that testing Hamiltonicity in the bounded-degree graph model requires a linear number of queries. This refers to both the path and the cycle versions of the problem, and similar results hold also for the directed analogues.
In addition, we present an alternative proof for the known fact that ... more >>>

In this work, we resolve the query complexity of global minimum cut problem for a graph by designing a randomized algorithm for approximating the size of minimum cut in a graph, where the graph can be accessed through local queries like \textsc{Degree}, \textsc{Neighbor}, and \textsc{Adjacency} queries.

Given $\epsilon \in (0,1)$, ... more >>>

Property testers are fast randomized algorithms whose task is to distinguish between inputs satisfying some predetermined property ${\cal P}$ and those that are far from satisfying it. Since these algorithms operate by inspecting a small randomly selected portion of the input, the most natural property one would like to be ... more >>>