A Large Scale Dataset for the Evaluation of Ontology Matching Systems

Recently, the number of ontology matching techniques and systems has increased significantly. This makes the issue of their evaluation and comparison more severe. One of the challenges of the ontology matching evaluation is in building large scale evaluation datasets. In fact, the number of possible correspondences between two ontologies grows quadratically with respect to the numbers of entities in these ontologies. This often makes the manual construction of the evaluation datasets demanding to the point of being infeasible for large scale matching tasks. In this paper we present an ontology matching evaluation dataset composed of thousands of matching tasks, called TaxME2. It was built semi-automatically out of the Google, Yahoo and Looksmart web directories. We evaluated TaxME2 by exploiting the results of almost two dozen of state of the art ontology matching systems. The experiments indicate that the dataset possesses the desired key properties, namely it is error-free, incremental, discriminative, monotonic, and hard for the state of the art ontology matching systems. The paper has been accepted for publication in "The Knowledge Engineering Review", Cambridge Universty Press (ISSN: 0269-8889, EISSN: 1469-8005)

The Complexity of Approximately Counting Stable Roommate Assignments

We investigate the complexity of approximately counting stable roommate assignments in two models: (i) the $k$-attribute model, in which the preference lists are determined by dot products of "preference vectors" with "attribute vectors" and (ii) the $k$-Euclidean model, in which the preference lists are determined by the closeness of the "positions" of the people to their "preferred positions". Exactly counting the number of assignments is #P-complete, since Irving and Leather demonstrated #P-completeness for the special case of the stable marriage problem. We show that counting the number of stable roommate assignments in the $k$-attribute model ($k \geq 4$) and the 3-Euclidean model($k \geq 3$) is interreducible, in an approximation-preserving sense, with counting independent sets (of all sizes) (#IS) in a graph, or counting the number of satisfying assignments of a Boolean formula (#SAT). This means that there can be no FPRAS for any of these problems unless NP=RP. As a consequence, we infer that there is no FPRAS for counting stable roommate assignments (#SR) unless NP=RP. Utilizing previous results by the authors, we give an approximation-preserving reduction from counting the number of independent sets in a bipartite graph (#BIS) to counting the number of stable roommate assignments both in the 3-attribute model and in the 2-Euclidean model. #BIS is complete with respect to approximation-preserving reductions in the logically-defined complexity class #RH\Pi_1. Hence, our result shows that an FPRAS for counting stable roommate assignments in the 3-attribute model would give an FPRAS for all of #RH\Pi_1. We also show that the 1-attribute stable roommate problem always has either one or two stable roommate assignments, so the number of assignments can be determined exactly in polynomial time

Algoritma matching bobot maskimum dalam graph bipartit komplit berboto

ABSTRAK Suatu matching dalam graph G adalah subgraph 1-regular pada G yang disebabkan oleh kumpulan dart pasangan garis yang tidak adjacent. Suatu matching merupakan matching maksimum bila matching tersebut mempunyai harga pokok maksimum. Matching dalam graph bipartit merupakan matching maksimum apabila tidak adanya path perluasart yang berkenaan dengan matching tersebut. Matching yang mempunyai bobot maksimum disebut matching bobot maksimum. Matching bobot maksimum dalam graph bipartit komplit berbobot diperoleh dengan mencari matching maksimum dalam subgraph pada graph bipartit komplit berbobot, kemudian dibangun sampai didapatkan matching perfek atau setiap titik dalam V merupakan titik matched. A matching in a graph G is a 1-regular subgraph of G, that is, a subgraph induced _by a collection of pairwise nonadjacent edges. A matching is called maximum matching if the matching have maximum cardinality. A matching in a bipartite graphs is a maximum matching if there exists no augmenting path. A matching in which the sum of the weights of maximum its edges is called maximum weight matching. A maximum weight matching in weighted complete bipartite graphs is got to find maximum matching in subgraph to weighted complete bipartite graphs, further its construct to arrived is got perfec matching or each vertex in V is matched vertex

Minimal Envy and Popular Matchings

We study ex-post fairness in the object allocation problem where objects are valuable and commonly owned. A matching is fair from individual perspective if it has only inevitable envy towards agents who received most preferred objects -- minimal envy matching. A matching is fair from social perspective if it is supported by majority against any other matching -- popular matching. Surprisingly, the two perspectives give the same outcome: when a popular matching exists it is equivalent to a minimal envy matching. We show the equivalence between global and local popularity: a matching is popular if and only if there does not exist a group of size up to 3 agents that decides to exchange their objects by majority, keeping the remaining matching fixed. We algorithmically show that an arbitrary matching is path-connected to a popular matching where along the path groups of up to 3 agents exchange their objects by majority. A market where random groups exchange objects by majority converges to a popular matching given such matching exists. When popular matching might not exist we define most popular matching as a matching that is popular among the largest subset of agents. We show that each minimal envy matching is a most popular matching and propose a polynomial-time algorithm to find them

Matching Logic

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values that match it), in contrast to FOL where functions and predicates map into a regular domain. Matching logic uniformly generalizes several logical frameworks important for program analysis, such as: propositional logic, algebraic specification, FOL with equality, modal logic, and separation logic. Patterns can specify separation requirements at any level in any program configuration, not only in the heaps or stores, without any special logical constructs for that: the very nature of pattern matching is that if two structures are matched as part of a pattern, then they can only be spatially separated. Like FOL, matching logic can also be translated into pure predicate logic with equality, at the same time admitting its own sound and complete proof system. A practical aspect of matching logic is that FOL reasoning with equality remains sound, so off-the-shelf provers and SMT solvers can be used for matching logic reasoning. Matching logic is particularly well-suited for reasoning about programs in programming languages that have an operational semantics, but it is not limited to this

Color Matching

We consider the problem of creating paint of a certain target color by mixing colorants. Although a large number of colorants are available, in practice it is only allowed to use a limited number. We focus on the problem of selecting the right subset of colorants