Related papers: The complexity of approximating averages on bounde…
The independent set polynomial is important in many areas. For every integer $\Delta\geq 2$, the Shearer threshold is the value $\lambda^*(\Delta)=(\Delta-1)^{\Delta-1}/\Delta^{\Delta}$ . It is known that for $\lambda < -…
Over the past decades, a fascinating computational phase transition has been identified in sampling from Gibbs distributions. Though, the computational complexity at the critical point remains poorly understood, as previous algorithmic and…
For graphs $G$ and $H$, we say that $G$ is $H$-free if it does not contain $H$ as an induced subgraph. Already in the early 1980s Alekseev observed that if $H$ is connected, then the \textsc{Max Weight Independent Set} problem (MWIS)…
For a fixed set ${\cal H}$ of graphs, a graph $G$ is ${\cal H}$-subgraph-free if $G$ does not contain any $H \in {\cal H}$ as a (not necessarily induced) subgraph. A recently proposed framework gives a complete classification on ${\cal…
We consider the algorithmic problem of finding large \textit{balanced} independent sets in sparse random bipartite graphs, and more generally the problem of finding independent sets with specified proportions of vertices on each side of the…
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…
The problem of minimizing a polynomial over the standard simplex is one of the basic NP-hard nonlinear optimization problems --- it contains the maximum clique problem in graphs as a special case. It is known that the problem allows a…
In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of…
A graph is called $P_t$-free} if it does not contain a $t$-vertex path as an induced subgraph. While $P_4$-free graphs are exactly cographs, the structure of $P_t$-free graphs for $t \geq 5$ remains little understood. On one hand, classic…
We show that for any $\Delta \geq 3$, there is no bound computable from $(\varepsilon, r)$ on the size of a graph required to approximate a graph of maximum degree at most $\Delta$ up to $\varepsilon$ error in $r$-neighborhood statistics.…
We introduce a new conjecture on the computational hardness of detecting random lifts of graphs: we claim that there is no polynomial-time algorithm that can distinguish between a large random $d$-regular graph and a large random lift of a…
In the Ising model, we consider the problem of estimating the covariance of the spins at two specified vertices. In the ferromagnetic case, it is easy to obtain an additive approximation to this covariance by repeatedly sampling from the…
We bound the performance guarantees that follow from Tur\'an-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, a randomized approach of Boppana forms a simple 1-round distributed algorithm, as…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
The all pairs shortest path problem (APSP) is one of the foundational problems in computer science. For weighted dense graphs on $n$ vertices, no truly sub-cubic algorithms exist to compute APSP exactly even for undirected graphs. This is…
Max Independent Set (MIS) is a paradigmatic problem in theoretical computer science and numerous studies tackle its resolution by exact algorithms with non-trivial worst-case complexity. The best such complexity is, to our knowledge, the…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
Counting independent sets on bipartite graphs (#BIS) is considered a canonical counting problem of intermediate approximation complexity. It is conjectured that #BIS neither has an FPRAS nor is as hard as #SAT to approximate. We study #BIS…