Related papers: On The Multiparty Communication Complexity of Test…
We study the problem of recognizing the cluster structure of a graph in the framework of property testing in the bounded degree model. Given a parameter $\varepsilon$, a $d$-bounded degree graph is defined to be $(k, \phi)$-clusterable, if…
Every triangle-free planar graph on n vertices has an independent set of size at least (n+1)/3, and this lower bound is tight. We give an algorithm that, given a triangle-free planar graph G on n vertices and an integer k>=0, decides…
We consider a quantum and classical version multi-party function computation problem with $n$ players, where players $2, \dots, n$ need to communicate appropriate information to player 1, so that a "generalized" inner product function with…
We prove that any triangle-free graph on $n$ vertices with minimum degree at least $d$ contains a bipartite induced subgraph of minimum degree at least $d^2/(2n)$. This is sharp up to a logarithmic factor in $n$. Relatedly, we show that the…
We study quantum communication protocols, in which the players' storage starts out in a state where one qubit is in a pure state, and all other qubits are totally mixed (i.e. in a random state), and no other storage is available (for…
I present a simple two-party quantum communication complexity protocol with higher success rate than the best possible classical protocol for the same task. The quantum protocol is shown to be equivalent to a quantum non-locality test,…
We study the problem of testing conductance in the setting of distributed computing and give a two-sided tester that takes $\mathcal{O}(\log(n) / (\epsilon \Phi^2))$ rounds to decide if a graph has conductance at least $\Phi$ or is…
We consider the well-known problem of enumerating all triangles of an undirected graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges, $M<E$ the size of internal memory, and…
Counting triangles in a graph and incident to each vertex is a fundamental and frequently considered task of graph analysis. We consider how to efficiently do this for huge graphs using massively parallel distributed-memory machines.…
We give a distributed algorithm in the {\sf CONGEST} model for property testing of planarity with one-sided error in general (unbounded-degree) graphs. Following Censor-Hillel et al. (DISC 2016), who recently initiated the study of property…
We consider the corner-stone broadcast task with an adaptive adversary that controls a fixed number of $t$ edges in the input communication graph. In this model, the adversary sees the entire communication in the network and the random…
The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…
In quantum information, nonlocal games are particularly useful for differentiating classical, quantum, and non-signalling correlations. An example of differentiation is given by the principle of no-collapse of communication complexity,…
A tournament is a complete directed graph. A king in a tournament is a vertex v such that every other vertex is reachable from v via a path of length at most 2. It is well known that every tournament has at least one king, one of which is a…
We present two new quantum algorithms that either find a triangle (a copy of $K_{3}$) in an undirected graph $G$ on $n$ nodes, or reject if $G$ is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes…
We revisit the algorithmic problem of finding a triangle in a graph (\textsc{Triangle Detection}), and examine its relation to other problems such as \textsc{3Sum}, \textsc{Independent Set}, and \textsc{Graph Coloring}. We obtain several…
In this paper, we study distributed graph algorithms in networks in which the nodes have a limited communication capacity. Many distributed systems are built on top of an underlying networking infrastructure, for example by using a virtual…
This paper proposes $\mathbf{C}$ommunication efficient $\mathbf{RE}$cursive $\mathbf{D}$istributed estimati$\mathbf{O}$n algorithm, $\mathcal{CREDO}$, for networked multi-worker setups without a central master node. $\mathcal{CREDO}$ is…
Independent samples from an unknown probability distribution $\bf p$ on a domain of size $k$ are distributed across $n$ players, with each player holding one sample. Each player can communicate $\ell$ bits to a central referee in a…
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…