Process mining techniques have recently received notable attention in the literature; for their ability to assist in the (re)design of complex processes by automatically discovering models that explain the events registered in some log traces provided as input. Following this line of research, the paper investigates an extension of such basic approaches, where the identification of different variants for the process is explicitly accounted for, based on the clustering of log traces. Indeed, modeling each group of similar executions with a different schema allows us to single out "conformant" models, which, specifically, minimize the number of modeled enactments that are extraneous to the process semantics. Therefore, a novel process mining framework is introduced and some relevant computational issues are deeply studied. As finding an exact solution to such an enhanced process mining problem is proven to require high computational costs, in most practical cases, a greedy approach is devised. This is founded on an iterative, hierarchical, refinement of the process model, where, at each step, traces sharing similar behavior patterns are clustered together and equipped with a specialized schema. The algorithm guarantees that each refinement leads to an increasingly sound mDdel, thus attaining a monotonic search. Experimental results evidence the validity of the approach with respect to both effectiveness and scalability

In this paper the problem of minimal representations for particular classes of directed hypergraphs is analyzed. Various concepts of minimal representations of directed hypergraphs (called minimal equivalent hypergraphs) are introduced as extensions to the concepts of transitive reduction and minimum equivalent graph of directed graphs. In particular, we consider equivalent hypergraphs which are minimal with respect to all parameters which may be adopted to characterize a given hypergraph (number of hyperarcs, number of adjacency lists required for the representation, length of the overall description,etc.). The relationships among the various concepts of minimality are discussed and their computational properties are analyzed. In order to derive such results, a graph representation of hypergraphs is introduced.

In a distributed database system the partitioning and allocation of the database over the processor nodes of the network can be a critical aspect of the database design effort. In this paper we develop and evaluate algorithms that perform this task in a computationally feasible manner. The network we consider is characterized by a relatively high communication bandwidth, considering the processing and input output capacities in its processors. Such a balance is typical if the processors are connected via busses or local networks. The common constraint that transactions have a specific root node no longer exists, so that there are more distribution choices. However, a poor distribution leads to less efficient computation, higher costs, and higher loads in the nodes or in the communication network so that the system may not be able to handle the required set of transactions. Our approach is to first split the database into fragments which constitute appropriate units for allocation. The fragments to be allocated are selected based on maximal benefit criteria using a greedy heuristic. The assignment to processor nodes uses a first-fit algorithm. The complete algorithm, called GFF, is stated in a procedural form. The complexity of the problem and of its candidate solutions are analyzed and several interesting relationships are proven. Alternate benefit metrics are considered, since the execution cost of the allocation procedure varies by orders of magnitude with the alternatives of benefit evaluation. A mixed benefit evaluation strategy is eventually proposed. A model for evaluation is presented. Two of the strategies are experimentally evaluated, and the reported results support the discussion. The approach should be suitable for other cases where resources have to be allocated subject to resource constraints.