Related papers: The Priority Lattice
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…
A nice factorization is given for the characteristic polynomials of intervals in some posets of leaf-labeled forests of rooted binary trees.
Given a classification model and a prediction for some input, there are heuristic strategies for ranking features according to their importance in regard to the prediction. One common approach to this task is rooted in propositional logic…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
We provide a direct proof that a finite graded lattice with a maximal chain of left modular elements is supersolvable. This result was first established via a detour through EL-labellings in [McNamara-Thomas] by combining results of…
We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning…
'Tree-based' phylogenetic networks proposed by Francis and Steel have attracted much attention of theoretical biologists in the last few years. At the heart of the definitions of tree-based phylogenetic networks is the notion of 'support…
This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that…
The Li-Chao tree (LICT) was first introduced in lecture as an efficient data structure for dynamic lower envelope maintenance. In the years since, it has achieved widespread adoption within the competitive programming community, yet no…
An important capability of autonomous multi-robot systems is to prevent collision among the individual robots. One approach to this problem is to plan conflict-free trajectories and let each of the robots follow its pre-planned trajectory.…
We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space $\mathcal{X}$ and the goal is to order all…
We introduce the lazy search tree data structure. The lazy search tree is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and…
In this paper, we present a probabilistic self-balancing dictionary data structure for massive data sets, and prove expected amortized I/O-optimal bounds on the dictionary operations. We show how to use the structure as an I/O-optimal…
We construct a homotopy initial functor from the partition complex of a finite set $A$ to a category of trees with leaves labelled by $A$. As an application, this provides an equivalence between different bar constructions of an operad. In…
This is an introduction to the M\"obius function of a poset. The chief novelty is in the exposition. We show how order-preserving maps from one poset to another can be used to relate their M\"obius functions. We derive the basic results on…
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our description is local, which offers the potential to speed up…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
Ranking bit patterns -- finding the index of a given pattern in an ordered sequence -- is a major bottleneck scaling up numerical quantum many-body calculations, as fermionic and hard-core bosonic states translate naturally to bit patterns.…