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We provide universally-optimal distributed graph algorithms for $(1+\varepsilon)$-approximate shortest path problems including shortest-path-tree and transshipment. The universal optimality of our algorithms guarantees that, on any $n$-node…
The main results of this paper are (I) a simulation algorithm which, under quite general constraints, transforms algorithms running on the Congested Clique into algorithms running in the MapReduce model, and (II) a distributed…
Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of…
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…
We propose ODTE, a new ensemble that uses oblique decision trees as base classifiers. Additionally, we introduce STree, the base algorithm for growing oblique decision trees, which leverages support vector machines to define hyperplanes…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
Parallel thinking has emerged as a new paradigm for large reasoning models (LRMs) in tackling complex problems. Recent methods leverage Reinforcement Learning (RL) to enhance parallel thinking, aiming to address the limitations in…
Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set;…
In this paper, we show a connection between a certain online low-congestion routing problem and an online prediction of graph labeling. More specifically, we prove that if there exists a routing scheme that guarantees a congestion of…
Classical path search assumes complete graphs and scalar optimization metrics, yet real infrastructure networks are incomplete and require multi-dimensional evaluation. We introduce the concept of traversal: a generalization of paths that…
We address the problem of mitigating damage to a power grid following a storm by managing a vehicle that has to be routed while simultaneously performing two tasks: learning about damage from the grid (which requires direct observation) and…
Rapidly Exploring Random Trees (RRT) is one of the most widely used algorithms for motion planning in the field of robotics. To reduce the exploration time, RRT-Connect was introduced where two trees are simultaneously formed and eventually…
We consider the problem of computing compact routing tables for a (weighted) planar graph $G:= (V, E,w)$ in the PRAM, CONGEST, and the novel HYBRID communication model. We present algorithms with polylogarithmic work and communication that…
A \emph{metric tree embedding} of expected \emph{stretch~$\alpha \geq 1$} maps a weighted $n$-node graph $G = (V, E, \omega)$ to a weighted tree $T = (V_T, E_T, \omega_T)$ with $V \subseteq V_T$ such that, for all $v,w \in V$,…
Distance labeling schemes are schemes that label the vertices of a graph with short labels in such a way that the distance between any two vertices $u$ and $v$ can be determined efficiently by merely inspecting the labels of $u$ and $v$,…
We consider the problem of routing a data packet through the visibility graph of a polygonal domain $P$ with $n$ vertices and $h$ holes. We may preprocess $P$ to obtain a label and a routing table for each vertex of $P$. Then, we must be…
The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…
We present a novel heuristic algorithm for routing optimization on complex networks. Previously proposed routing optimization algorithms aim at avoiding or reducing link overload. Our algorithm balances traffic on a network by minimizing…
Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…
Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic…