In this report an entropy bound on the memory size is given for a compression method of leaf-labeled trees. The compression converts the tree into a Directed Acyclic Graph (DAG) by merging isomorphic subtrees. I. COUPON COLLECTOR’S PROBLEM WITH ARBITRARY COUPON PROBABILITIES Given a set of C coupons, where δ = |C| denotes the number of coupons. At each draw po denotes the probability for gettin...

Given an untrimmed video, temporal sentence localization (TSL) aims to localize a specific segment according given query. Though respectable works have made decent achievements in this task, they severely rely on dense video frame annotations, which require tremendous amount of human effort collect. In paper, we target another more practical and challenging setting: one-shot (one-shot TSL), lea...

Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We construct a bijection between these two combinatorial objects and study the therefrom arising connections of certain parameters. Furthermore, we show central limit t...

The notions of γ and β-acyclicity are two classic generalizations of the acyclicity of graphs to hypergraphs. They satisfy the property that, if a hypergraph is γ-acyclic then it is β-acyclic, and the reverse is false. We give some new properties concerning these notions. First we show that we can strictly insert another notion of acyclicity between them, namely the fact of having a join tree w...

Several applications require management of data which is spatially dynamic, e.g., tracking of battle ships or moving cells in a blood sample. The capability of handling the temporal aspect, i.e., the history of such type of data, is also important. This paper presents and evaluates three temporal extensions of the R-tree, the 3D R-tree, the 2+3 R-tree and the HR-tree, which are capable of index...

Suppose that C = {cij : i, j ≥ 1} is a collection of i.i.d. nonnegative continuous random variables and suppose T is a rooted, directed tree on vertices labelled 1,2,. . . ,n. Then the ‘cost’ of T is defined to be c(T ) = ∑ (i,j)∈T cij , where (i, j) is denotes the directed edge from i to j in the tree T . Let Tn denote the ‘optimal’ tree, i.e. c(Tn) = min{c(T ) : T is a directed, rooted tree i...

We consider two symbolic approaches to bounded model checking (BMC) of distributed time Petri nets (DTPNs). We focus on the properties expressed in Linear Temporal Logic without the neXt-time operator (LTL−X) and the existential fragment of Computation Tree Logic without the neXt-time operator (ECTL−X). We give a translation of BMC to SAT and describe a BDD-based BMC for both LTL−X and ECTL−X. ...

With the ever-growing digital libraries and video databases, it is increasingly important to understand and mine the knowledge from video database automatically. Video association mining is a relatively new and emerging research trend used to discover and describe interesting patterns in video. The traditional classical association rule mining algorithms can not apply directly to the video. It ...