Symmetry widely exists in many complex and real-world networks, with flower networks sunflower being two richly symmetric having practical applications due to their special structures. The number of subtrees (the subtree index) is closely related the reliable network design. Using a generating function, structural analysis techniques, auxiliary structure introduction, this paper presents functi...

A plane drawing of a graph is called a floorplan if every face (including the outer face) is a rectangle. A based floorplan is a floorplan with a designated base line segment on the outer face. In this paper we give a simple algorithm to generate all based floorplans with at most n faces. The algorithm uses O(n) space and generates such floorplans in O(1) time per floorplan without duplications...

In 1966, Rosa introduced, among others, αand β-labelings as tools to solve the isomorphic decomposition problem of the complete graph. Ten years later, Sheppard calculated the number of αand β-labeled graphs with n edges. In this paper we use an extended version of the adjacency matrix of a graph to determine the number of gracefully labeled graphs with n edges; furthermore, we also calculate t...

We provide a semi-grammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This method is complete in the sense that each normal proof-term of the formula is produced by some scheme generated by the grammar. As a corollary, we get a simi...

In a distributed storage systems (DSS), regenerating codes are used to optimize bandwidth in the repair process of a failed node. To optimize other DSS parameters such as computation and disk I/O, Distributed Replication-based Simple Storage (Dress) Codes consisting of an inner Fractional Repetition (FR) code and an outer MDS code are commonly used. Thus constructing FR codes is an important re...

MOTIVATION Next-generation sequencing techniques have facilitated a large-scale analysis of human genetic variation. Despite the advances in sequencing speed, the computational discovery of structural variants is not yet standard. It is likely that many variants have remained undiscovered in most sequenced individuals. RESULTS Here, we present a novel internal segment size based approach, whi...

We propose a generic model for the “weighted voting” aggregation step performed by several methods in supervised classification. Further, we construct an algorithm to enumerate the number of distinct aggregate classifiers that arise in this model. When there are only two classes in the classification problem, we show that a class of functions that arises from aggregate classifiers coincides wit...

Given a collection of leaf-labeled trees on a common leafset and a fraction f in (1/2,1], a frequent subtree (FST) is a subtree isomorphically included in at least fraction f of the input trees. The well-known maximum agreement subtree (MAST) problem identifies FST with f = 1 and having the largest number of leaves. Apart from its intrinsic interest from the algorithmic perspective, MAST has pr...