Related papers: Low Degree Hardness for Broadcasting on Trees

A standard way of justifying that a certain probabilistic property holds in a system is to provide a witnessing subsystem (also called critical subsystem) for the property. Computing minimal witnessing subsystems is NP-hard already for…

This paper proposes a new detection algorithm for MIMO communication systems employing high order QAM constellations. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete graph. Hence, a straightforward…

The semi-streaming model is a variant of the streaming model frequently used for the computation of graph problems. It allows the edges of an $n$-node input graph to be read sequentially in $p$ passes using $\tilde{O}(n)$ space. In this…

We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has $k$ data packets to broadcast, and it suffices that a large fraction of the network…

Broadcasting and convergecasting are pivotal services in distributed systems, in particular, in wireless ad-hoc and sensor networks, which are characterized by time- varying communication graphs. We study the question of whether it is…

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on…

We consider growing random networks $\{\mathcal G_n\}_{n \ge 1}$ where, at each time, a new vertex attaches itself to a collection of existing vertices via a fixed number $m \ge 1$ of edges, with probability proportional to an attachment…

Treedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a $2^{O(k^2)} n$-time exact algorithm and a polynomial-time $O(\text{OPT} \log^{3/2}…

We present a linear programming based algorithm for computing a spanning tree $T$ of a set $P$ of $n$ points in $\Re^d$, such that its crossing number is $O(\min(t \log n, n^{1-1/d}))$, where $t$ the minimum crossing number of any spanning…

The problem considered is the following. Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, compute a low-weight spanning tree such that the degree of each vertex is at most its specified…

Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…

We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…

It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif…

A topic propagating in a social network reaches its tipping point if the number of users discussing it in the network exceeds a critical threshold such that a wide cascade on the topic is likely to occur. In this paper, we consider the task…

The degree-d spanning tree problem asks for a minimum-weight spanning tree in which the degree of each vertex is at most d. When d=2 the problem is TSP, and in this case, the well-known Christofides algorithm provides a 1.5-approximation…

Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

We continue a line of work on extracting random bits from weak sources that are generated by simple processes. We focus on the model of locally samplable sources, where each bit in the source depends on a small number of (hidden) uniformly…

Phylogenetic networks generalize phylogenetic trees by representing reticulate evolution. Tree-based networks and their support trees have been extensively studied, but not all networks are tree-based. To measure how far such networks are…

Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…

Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…