Related papers: Low Degree Hardness for Broadcasting on Trees
We consider the problem of collaborative tree exploration posed by Fraigniaud, Gasieniec, Kowalski, and Pelc where a team of $k$ agents is tasked to collectively go through all the edges of an unknown tree as fast as possible. Denoting by…
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…
The low-degree polynomial framework has been highly successful in predicting computational versus statistical gaps for high-dimensional problems in average-case analysis and machine learning. This success has led to the low-degree…
We consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…
We consider the problem of deterministic broadcasting in radio networks when the nodes have limited knowledge about the topology of the network. We show that for every deterministic broadcasting protocol there exists a network, of radius 2,…
Message passing type algorithms such as the so-called Belief Propagation algorithm have recently gained a lot of attention in the statistics, signal processing and machine learning communities as attractive algorithms for solving a variety…
We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML…
Until recently, the fastest distributed MIS algorithm, even for simple graphs, e.g., unoriented trees has been the simple randomized algorithm discovered the 80s. This algorithm (commonly called Luby's algorithm) computes an MIS in $O(\log…
A spanning tree $T$ of graph $G$ is a $\rho$-approximate universal Steiner tree (UST) for root vertex $r$ if, for any subset of vertices $S$ containing $r$, the cost of the minimal subgraph of $T$ connecting $S$ is within a $\rho$ factor of…
We present new distributed quantum algorithms for fundamental distributed computing problems, namely, leader election, broadcast, Minimum Spanning Tree (MST), and Breadth-First Search (BFS) tree, in arbitrary networks. These algorithms are…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
A spanning tree of a network or graph is a subgraph that connects all nodes with the least number or weight of edges. The spanning tree is one of the most straightforward techniques for network simplification and sampling, and for…
In the Priority Steiner Tree (PST) problem, we are given an undirected graph $G=(V,E)$ with a source $s \in V$ and terminals $T \subseteq V \setminus \{s\}$, where each terminal $v \in T$ requires a nonnegative priority $P(v)$. The goal is…
Vector autoregression has been widely used for modeling and analysis of multivariate time series data. In high-dimensional settings, model parameter regularization schemes inducing sparsity yield interpretable models and achieved good…
The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture.…
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…
In the $k$-dispersion problem, we need to select $k$ nodes of a given graph so as to maximize the minimum distance between any two chosen nodes. This can be seen as a generalization of the independent set problem, where the goal is to…