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Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is as convex as possible, given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time algorithm, but efficient methods to decide tightness are only known in the trivial setting of triangulated surfaces. In this article, we present a new polynomial time procedure to decide tightness for triangulations of $3$-manifolds -- a problem which previously was thought to be hard. Furthermore, we describe an algorithm to decide general tightness in the case of $4$-dimensional combinatorial manifolds which is fixed parameter tractable in the treewidth of the $1$-skeletons of their vertex links, and we present an algorithm to decide $mathbb{F}_2$-tightness for weak pseudomanifolds $M$ of arbitrary but fixed dimension which is fixed parameter tractable in the treewidth of the dual graph of $M$.
Given two sets $S$ and $T$ of points in the plane, of total size $n$, a {many-to-many} matching between $S$ and $T$ is a set of pairs $(p,q)$ such that $pin S$, $qin T$ and for each $rin Scup T$, $r$ appears in at least one such pair. The {cost of a
In this paper, we propose efficient probabilistic algorithms for several problems regarding the autocorrelation spectrum. First, we present a quantum algorithm that samples from the Walsh spectrum of any derivative of $f()$. Informally, the autocorre
Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of consecutive edges in the ordering -- an angle -- such that each edge parti
An $h$-queue layout of a graph $G$ consists of a linear order of its vertices and a partition of its edges into $h$ queues, such that no two independent edges of the same queue nest. The minimum $h$ such that $G$ admits an $h$-queue layout is the que
Ailon et al. [SICOMP11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances $x_1,cdots,x_n$ follow some unknown emph{product distribution}. That is, $x_i$ comes from a fixed unknown distribution $ma