Related papers: Dynamic Products of Ranks
The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
In this paper we describe a new data structure that supports orthogonal range reporting queries on a set of points that move along linear trajectories on a $U\times U$ grid. The assumption that points lie on a $U\times U$ grid enables us to…
As e-commerce expands, delivering real-time personalized recommendations from vast catalogs poses a critical challenge for retail platforms. Maximizing revenue requires careful consideration of both individual customer characteristics and…
Data-structure dynamization is a general approach for making static data structures dynamic. It is used extensively in geometric settings and in the guise of so-called merge (or compaction) policies in big-data databases such as Google…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider…
We consider a manufacturing plant that purchases raw materials for product assembly and then sells the final products to customers. There are M types of raw materials and K types of products, and each product uses a certain subset of raw…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
A new characterization for power function distributions is obtained which is based on products of order statistics. This result may be considered as a generalization of some recent results for contractions. We note that in this new result…
An emerging paradigm proposes that neural computations can be understood at the level of dynamical systems that govern low-dimensional trajectories of collective neural activity. How the connectivity structure of a network determines the…
Discrete-time regulatory networks are dynamical systems on directed graphs, with a structure inspired on natural systems of interacting units. There is a natural notion of determination amongst vertices, which we use to classify the nodes…
We present a dynamic data structure for representing binary $n\times n$ matrices that are $d$-twin-ordered, for a~fixed parameter $d$. Our structure supports cell queries and single-cell updates both in $\Oh(\log \log n)$ expected worst…
Rankings play a crucial role in decision-making. However, if minor changes to items significantly alter their rankings, the quality of the decisions being made can be compromised. The stability of ranking is a measure used to assess how…
We present the first deterministic data structures for maintaining approximate minimum vertex cover and maximum matching in a fully dynamic graph $G = (V,E)$, with $|V| = n$ and $|E| =m$, in $o(\sqrt{m}\,)$ time per update. In particular,…
In the setting of DynFO, dynamic programs update the stored result of a query whenever the underlying data changes. This update is expressed in terms of first-order logic. We introduce a strategy for constructing dynamic programs that…
Proportional ranking rules aggregate approval-style preferences of agents into a collective ranking such that groups of agents with similar preferences are adequately represented. Motivated by the application of live Q&A platforms, where…
Rank-width is a width parameter of graphs describing whether it is possible to decompose a graph into a tree-like structure by `simple' cuts. This survey aims to summarize known algorithmic and structural results on rank-width of graphs.
From the viewpoint of networks, a ranking system for players or teams in sports is equivalent to a centrality measure for sports networks, whereby a directed link represents the result of a single game. Previously proposed network-based…
For a set $P$ of $n$ points in the plane and a value $r > 0$, the unit-disk range reporting problem is to construct a data structure so that given any query disk of radius $r$, all points of $P$ in the disk can be reported efficiently. We…