Related papers: Lexico-minimum Replica Placement in Multitrees
The Minimum Branch Vertices Spanning Tree problem aims to find a spanning tree $T$ in a given graph $G$ with the fewest branch vertices, defined as vertices with a degree three or more in $T$. This problem, known to be NP-hard, has…
Motion planning problems have been studied by both the robotics and the controls research communities for a long time, and many algorithms have been developed for their solution. Among them, incremental sampling-based motion planning…
Kinodynamic motion planning is concerned with computing collision-free trajectories while abiding by the robot's dynamic constraints. This critical problem is often tackled using sampling-based planners (SBPs) that explore the robot's…
We study discrete random walks on the NFSFT and provide new methods to calculate the analytic solutions of the MFPT for any pair of nodes, the MTT for any target node and MDT for any source node. Further more, using the MTT and the MDT as…
Distributed computing has become a common practice nowadays, where the recent focus has been given to the usage of smart networking devices with in-network computing capabilities. State-of-the-art switches with near-line rate computing and…
Write-optimized dictionaries are a class of cache-efficient data structures that buffer updates and apply them in batches to optimize the amortized cache misses per update. For example, a B^epsilon tree inserts updates as messages at the…
Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
Constructing a Depth First Search (DFS) tree is a fundamental graph problem, whose parallel complexity is still not settled. Reif showed parallel intractability of lex-first DFS. In contrast, randomized parallel algorithms (and more…
Linear arrangements of graphs are a well-known type of graph labeling and are found in many important computational problems, such as the Minimum Linear Arrangement Problem ($\texttt{minLA}$). A linear arrangement is usually defined as a…
We introduce a new problem in the domain of mobile robots, which we term dispersion. In this problem, $n$ robots are placed in an $n$ node graph arbitrarily and must coordinate with each other to reach a final configuration such that…
Decision trees are widely used for classification and regression tasks in a variety of application fields due to their interpretability and good accuracy. During the past decade, growing attention has been devoted to globally optimized…
The Random Projection Tree structures proposed in [Freund-Dasgupta STOC08] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTreeMax…
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…
Let $G$ be a simple graph on $n$ vertices. We consider the problem LIS of deciding whether there exists an induced subtree with exactly $i \leq n$ vertices and $\ell$ leaves in $G$. We study the associated optimization problem, that…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
Multitask learning and related areas such as multi-source domain adaptation address modern settings where datasets from $N$ related distributions $\{P_t\}$ are to be combined towards improving performance on any single such distribution…
Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…
Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through…
The inherent probabilistic nature of Large Language Models (LLMs) introduces an element of unpredictability, raising concerns about potential discrepancies in their output. This paper introduces an innovative approach aims to generate…
An important problem in evolutionary biology is to reconstruct the evolutionary history of a set $X$ of species. This history is often represented as a phylogenetic network, that is, a connected graph with leaves labelled by elements in $X$…