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The bounded degree complex $BD(G,\lambda)$ is a generalization of the matching complexes of a graph. In this paper, we show that the bounded degree complex of a forest is shellable, by using independence complexes of hypergraphs. We obtain…
We introduce a new compression scheme for labeled trees based on top trees. Our compression scheme is the first to simultaneously take advantage of internal repeats in the tree (as opposed to the classical DAG compression that only exploits…
Purpose: This paper presents an algorithm that can elicitate (infer) all or any combination of ELECTRE Tri-B parameters. For example, a decision-maker can maintain the values for indifference, preference, and veto thresholds, and our…
We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel…
We introduce a new class of tree-based models, P-Trees, for analyzing (unbalanced) panel of individual asset returns, generalizing high-dimensional sorting with economic guidance and interpretability. Under the mean-variance efficient…
Interpretability has become incredibly important as machine learning is increasingly used to inform consequential decisions. We propose to construct global explanations of complex, blackbox models in the form of a decision tree…
We recast dependency parsing as a sequence labeling problem, exploring several encodings of dependency trees as labels. While dependency parsing by means of sequence labeling had been attempted in existing work, results suggested that the…
It implicitly follows from the work of [Colbourn, El-Mallah: On two dual classes of planar graphs. Discrete Mathematics 80(1): 21-40 (1990)] that every planar partial 3-tree is a subgraph of a planar 3-tree. This fact has already enabled to…
The $B^{\epsilon}$-tree [Brodal and Fagerberg 2003] is a simple I/O-efficient external-memory-model data structure that supports updates orders of magnitude faster than B-tree with a query performance comparable to the B-tree: for any…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating the underlying large proof search spaces. While the…
The verification of liveness conditions is an important aspect of state-based rigorous methods. This article addresses the extension of the logic of Event-B to a powerful logic, in which properties of traces of an Event-B machine can be…
For decades, it was unknown how electron bifurcating systems in Nature prevented energy-wasting short-circuiting reactions that have large driving forces, so synthetic electron bifurcating molecular machines could not be designed and built.…
Small devices collecting data for agricultural, environmental, and industrial monitoring enable Internet of Things (IoT) applications. Given their critical role in data collection, there is a need for optimizations to improve on-device data…
We provide a description of the structure of $\aleph_0$-categorical trees and cycle-free partial orders. First the maximal branches of $\aleph_0$-categorical tree are examined, followed by the configuration of the ramification orders, which…
Search engines play a vital role in day to day life on internet. People use search engines to find content on internet. Cloud computing is the computing concept in which data is stored and accessed with the help of a third party server…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…
In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…
We consider the task of optimizing the B-tree data structure, used extensively in operating systems and databases, for sustainable usage on multi-level flash memory. Empirical evidence shows that this new flash memory tree, or FM Tree,…