ABSTRACT. The goal of the present work is to be able to compute efficiently with symbolically defined piece-wise functions.

ABSTRACT. EasyChair started in 2002 as a small collection of scripts helping the author to organise submission and reviewing for the conferences LPAR and CADE. Since then it has served over 40,000 conferences and nearly 1,500,000 users. The system has over 290,000 lines of source code and automates paper submission, reviewing, proceedings generation, publishing, conference registration and conference programme generation. Several new modules are under development.

The design and architecture of every very large Web service is unique, and EasyChair is not an exception. This talk overviews design features of EasyChair, which may be interesting for the software engineering community:

1. Highly agile development methodology
2. Design centred around a small number of concepts
3. Automatic generation of efficient and secure code
4. An object caching technique eliminating mismatch between objects and relational data
5. Server-side generation of client-side code
6. Automation of code management
7. Light-weight source code analysis
8. Automatic generation of documentation
9. Integrity constraint management

Nearly 50% of EasyChair code is now generated automatically. The high level of code management automation of EasyChair has allowed the author to increase the code size by around 50,000 lines in the last 12 months and also make the code easier to maintain and understand.

ABSTRACT. One of the newest molecular descriptors, the general sum-connectivity index of a graph G is defined as $\chi_\alpha(G)~=~\sum_{uv\in{E(G)}}(d(u)+d(v))^\alpha$, where $d(u)$ denotes the degree of vertex $u$ in $G$ and $\alpha$ is a real number. The aim of this paper is to determine the trees and the unicyclic graphs with $k$ pendant vertices that maximize the general sum-connectivity index for $\alpha\geq 1$, with $2\leq k

ABSTRACT. The Finitely Supported Mathematics represents the Zermelo-Fraenkel mathematics reformulated in the framework of invariant sets. We develop a theory of abstract interpretations which is consistent to the principles of constructing the Finitely Supported Mathematics. We first translate the notions of lattices and Galois connections into the framework of invariant sets, and then present their properties in terms of finitely supported objects. Later, we introduce the notions of invariant correctness relation and invariant representation function, we emphasize an equivalence between them, and we establish the relationship between these notions and invariant Galois connections.  Finally, we provide some widening and narrowing techniques in order to approximate
the least fixed points of finitely supported transition functions.

ABSTRACT. A combinatorial condition called well distributed occurrences, or WELLDOC for short, has been introduced recently. The proofs that WELLDOC property holds for the family of Sturmian words, and more generally, for Arnoux-Rauzy words are given in two papers by Balkova et al. The WELLDOC property for bounded bi-ideals is analysed in this paper. The existence of a 1-bounded bi-ideal over the finite alphabet that satisfies the WELLDOC property has been proved by the authors.

ABSTRACT. We present a denotational semantics designed with metric spaces and continuations for a simple concurrent language $\Lmb$ embodying a representative set of features encountered in membrane computing. $\Lmb$ is a multiset rewriting language. In $\Lmb$ multisets of objects are encapsulated in hierarchical structures of compartments, or regions, delimited by {\em{membranes}}. The behaviour of each membrane is specified by means of {\em{multiset rewriting rules}}. The semantics of parallel composition in $\Lmb$ is based on the concept of {\em{maximal parallelism}}. Computations proceed according to the multiset rewriting rules, nondeterministically choosing the rules and the objects. Membranes can be grouped into classes based on the rewriting rules that they encapsulate; $\Lmb$ also provides a primitive for membrane creation, or instantiation. In this sense, $\Lmb$ is similar to an object oriented language. We use continuations and a powerdomain construction to represent nondeterministic behavior. An element of a powerdomain is a collection of sequences of observables representing dynamic membrane structures. Our continuation semantics describes in a compositional manner the behavior of an $\Lmb$ program as a dynamic hierarchical system. As far as we know, this is the first paper that presents a metric denotational semantics for the combination of features embodied in $\Lmb$.

ABSTRACT. Monitoring cloud resources is an essential part of cloud computing, and although some effort has been made in this direction, monitoring security parameters is still an open issue. In this paper we propose a distributed system that is able to monitor, filter and store different network and host parameters related to the security of a system. The proposed system is decentralized, fault tolerant and highly parallel, those three attributes making it a perfect candidate for monitoring resources in a cloud environment. The system is build with multi tenancy in mind, but it can be deployed with success in single tenant environments as well.

ABSTRACT. The goal of our research is a combinatorial adaptation of the well-known k-means clustering algorithm to large-scale problems represented by graphs. Traditionally k-means is applied in a graph theoretic approach in a two-step fashion: First a metric on the set of the nodes is defined, then a standard k-means method is used on this metric space. In these approaches, however, the k-means algorithm itself does not use the inherent combinatorial structure of the graph, and the calculation on the metric space does not make possible to handle extra large graph problems. In this paper we propose a more natural combinatorial approach.

The basic points of the $k$-means algorithm is the definition of the "center" of a cluster, and the definition of a metric by which we can calculate the distance of a point from a given cluster, more exactly from its center. Let us note, that the concept of the "center" in the original algorithm serves as an approximation to speed up the algorithm and to avoid more complex calculations of the distance from multiple points of the cluster. In the graph-theoretic approach the concept of the "center" is less clear. Moreover, in the above mentioned classical two-step approaches, the proposed metrics are non-natural to the original problems. We propose several more natural combinatorial definitions for the "center" and for the distance metric.

In our first approach, if we are searching for graph clusters, we are searching for a subgraph of high density. From this point of view, the distance of a node can be characterized by the number of connections to a given subset of nodes. This leads us to the definition of a "center" as the whole cluster itself. The calculation of the proposed distance is quite simple, as we can use parallelism to calculate the intersection of the cluster and the neighbouring nodes of a node.

Another idea is to adopt coloring methodology to k-means. In that case we are interested in possibly big independent subsets. This approach leads us to another definition of the center: the largest independent spanned subgraph of a cluster -- we may call it the core of a cluster. The metric will be the "opposite" of the previous one: the less the connections to a core, the smaller the distance. Obviously, finding the biggest independent subset is an NP-hard problem, but the clusters will be much smaller, so it is practical to find it. Other possibility would be to use an approximation method. With this method we can find or quasi-coloring, or if the number of color classes (clusters) high enough it may lead us to a good approximative coloring. It is an interesting question to find out how good this coloring is in comparison with other greedy colorings.

The k-means algorithm can be adopted to parallel computers in a highly efficient way using the bulk synchronious parallel method, achieving near linear speedup even for high processor count. This method is related to the map-reduce way of parallelization using several map-reduce steps with a small cost communication reduction phase in between. The proposed graph algorithms obviously can be speed up using several thousands processors.

We implemented the proposed algorithms in C++ and MPI framework, and tested it on different inputs on the Finish Sisu computer up to 512 computing nodes with promising results.

ABSTRACT. Petri Nets (PN) are a well established formal model for distributed/concurrent systems. Classical PNs (both high and low level), even if Turing powerful, lack of features for representing in a natural way dynamical changes that may involve the system topology and behavior during lifecycle. Many different attempts to face this issue lead to the proposal of new PN extensions, among which those matching the so called "nets within nets" paradigm -in which tokens of a "base level" PN model are indeed objects representing nets- have become quite popular . In particular higher-order algebraic PNs have been recently proposed as a unifying framework for this interesting paradigm. In this paper we present a new approach rigorously based on classical spec-inscribed nets, which have a sound algebraic semantics, as an alternative to the "nets within nets" extensions. Even if inspired by the same principles, and sharing most of the goals, our approach implements a single modeling layer in a uniform way, and permits consolidated analysis techniques to be used. Our formalization relies on the well known OBJ specification language.