We investigate the problem of database equivalence which arises in database design process. We introduce a graph formalism for the treatment of this problem. More precisely, we represent Entity-Relationship schemes by a special kind of graphs (called JFD-graphs) and we give a simple and efficient algorithm for testing the equivalence of two schemes. In addition, we present a set of elementary o...

We define the analogue of linear equivalence of graph divisors for the rotorrouter model, and use it to prove polynomial time computability of some problems related to rotor-routing. Using the connection between linear equivalence for chip-firing and for rotor-routing, we prove that the number of rotor-router unicycle-orbits equals the order of the Picard group. We also show that the rotor-rout...

We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva in [CDPR12] between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the v0-reduced divisors (representatives of the equivalence classes) associated to...

Graph products are characterized by the existence of non-trivial equivalence relations on the edge set of a graph that satisfy a so-called square property. We investigate here a generalization, termed RSP-relations. The class of graphs with non-trivial RSP-relations in particular includes graph bundles. Furthermore, RSP-relations are intimately related with covering graph constructions. For K2,...

We offer an alternative to the standard formalisation of attributed graphs. We propose to represent an attributed graph as a graph with a marked sub-graph, in which the sub-graph represents the data domain, rather than as a tuple of graph and algebra. This is a general construction which can be shown to preserve adhesiveness of categories; it has the advantage of uniformity and gives more flexi...

Recall that last time we have introduced the set of weights Wt(n) ⊂ C and an equivalence relation ∼ on Wt(n). Our goal is to describe this set and this equivalence relation – the equivalence classes are in a natural bijection with Irr(Sn). The first step here is as follows. Pick a path P = V 1 → V 2 → . . . → V n in the branching graph and an integer k with 1 < k < n. We fix all vertices but V ...

We consider the problem of learning Bayesian network structures from complete data. In particular, we consider the enumeration of their k-best equivalence classes. We propose a new search space for A* search, called the EC graph, that facilitates the enumeration of equivalence classes, by representing the space of completed, partially directed acyclic graphs. We also propose a canonization of t...

Equality of expressions in lambda-calculi, higher-order programming languages, higher-order programming calculi and process calculi is defined as alpha-equivalence. Permutability of bindings in let-constructs and structural congruence axioms extend alpha-equivalence. We analyse these extended alpha-equivalences and show that there are calculi with polynomial time algorithms, that a multiple-bin...

In [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action of local Clifford operations on graph states in terms of a graph transformation rule, known in graph theory as local complementation. It was shown that two graph states are equivalent under the local Clifford group if and only if there exists a sequence of local complementations which relates their associated graphs. I...

We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible \backward" extensions of the above hyperbolic graph and considering them as the classes of a discrete equivalence relation on an appropriate compact space. Illustrating these tec...