Luciana S. Buriol

Preferential attachment in the growth of social networks: The internet encyclopedia Wikipedia

We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with those of the World Wide Web, despite the very different growth mechanism. In particular, we measure a scale-invariant distribution of the in and out degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users, who are responsible of its evolution, can act globally on the network.

Counting triangles in data streams

We present two space bounded random sampling algorithms that compute an approximation of the number of triangles in an undirected graph given as a stream of edges. Our first algorithm does not make any assumptions on the order of edges in the stream. It uses space that is inversely related to the ratio between the number of triangles and the number of triples with at least one edge in the induced subgraph, and constant expected update time per edge. Our second algorithm is designed for incidence streams (all edges incident to the same vertex appear consecutively). It uses space that is inversely related to the ratio between the number of triangles and length 2 paths in the graph and expected update time O(log|V|⋅(1+s⋅|V|/|E|)), where s is the space requirement of the algorithm. These results significantly improve over previous work [20, 8]. Since the space complexity depends only on the structure of the input graph and not on the number of nodes, our algorithms scale very well with increasing graph size and so they provide a basic tool to analyze the structure of large graphs. They have many applications, for example, in the discovery of Web communities, the computation of clustering and transitivity coefficient, and discovery of frequent patterns in large graphs.We have implemented both algorithms and evaluated their performance on networks from different application domains. The sizes of the considered graphs varied from about 8,000 nodes and 40,000 edges to 135 million nodes and more than 1 billion edges. For both algorithms we run experiments with parameter s=1,000, 10,000, 100,000, 1,000,000 to evaluate running time and approximation guarantee. Both algorithms appear to be time efficient for these sample sizes. The approximation quality of the first algorithm was varying significantly and even for s=1,000,000 we had more than 10% deviation for more than half of the instances. The second algorithm performed much better and even for s=10,000 we had an average deviation of less than 6% (taken over all but the largest instance for which we could not compute the number of triangles exactly).

Piecing together the NFV provisioning puzzle: Efficient placement and chaining of virtual network functions

Network Function Virtualization (NFV) is a promising network architecture concept, in which virtualization technologies are employed to manage networking functions via software as opposed to having to rely on hardware to handle these functions. By shifting dedicated, hardware-based network function processing to software running on commoditized hardware, NFV has the potential to make the provisioning of network functions more flexible and cost-effective, to mention just a few anticipated benefits. Despite consistent initial efforts to make NFV a reality, little has been done towards efficiently placing virtual network functions and deploying service function chains (SFC). With respect to this particular research problem, it is important to make sure resource allocation is carefully performed and orchestrated, preventing over- or under-provisioning of resources and keeping end-to-end delays comparable to those observed in traditional middlebox-based networks. In this paper, we formalize the network function placement and chaining problem and propose an Integer Linear Programming (ILP) model to solve it. Additionally, in order to cope with large infrastructures, we propose a heuristic procedure for efficiently guiding the ILP solver towards feasible, near-optimal solutions. Results show that the proposed model leads to a reduction of up to 25% in end-to-end delays (in comparison to chainings observed in traditional infrastructures) and an acceptable resource over-provisioning limited to 4%. Further, we demonstrate that our heuristic approach is able to find solutions that are very close to optimality while delivering results in a timely manner.

A New Memetic Algorithm for the Asymmetric Traveling Salesman Problem

This paper introduces a new memetic algorithm specialized for the asymmetric instances of the traveling salesman problem (ATSP). The method incorporates a new local search engine and many other features that contribute to its effectiveness, such as: (i) the topological organization of the population as a complete ternary tree with thirteen nodes; (ii) the hierarchical organization of the population in overlapping clusters leading to the special selection scheme; (iii) efficient data structures. Computational experiments are conducted on all ATSP instances available in the TSPLIB, and on a set of larger asymmetric instances with known optimal solutions. The comparisons show that the results obtained by our method compare favorably with those obtained by several other algorithms recently proposed for the ATSP.

Speeding Up Dynamic Shortest-Path Algorithms

Dynamic shortest-path algorithms update the shortest paths taking into account a change in an arc weight. This paper describes a new generic technique that allows the reduction of heap sizes used by several dynamic single-destination shortest-path algorithms. For unit weight changes, the updates can be done without heaps. These reductions almost always reduce the computational times for these algorithms. In computational testing, several dynamic shortest-path algorithms with and without the heap-reduction technique are compared. Speedups of up to a factor of 1.8 were observed using the heap-reduction technique on random weight changes and of over a factor of five on unit weight changes. We compare as well with Dijkstras algorithm, which recomputes the paths from scratch. With respect to Dijkstras algorithm, speedups of up to five orders of magnitude are observed.

Three-dimensional protein structure prediction

A long standing problem in structural bioinformatics is to determine the three-dimensional (3-D) structure of a protein when only a sequence of amino acid residues is given. Many computational methodologies and algorithms have been proposed as a solution to the 3-D Protein Structure Prediction (3-D-PSP) problem. These methods can be divided in four main classes: (a) first principle methods without database information; (b) first principle methods with database information; (c) fold recognition and threading methods; and (d) comparative modeling methods and sequence alignment strategies. Deterministic computational techniques, optimization techniques, data mining and machine learning approaches are typically used in the construction of computational solutions for the PSP problem. Our main goal with this work is to review the methods and computational strategies that are currently used in 3-D protein prediction.

A biased random-key genetic algorithm for road congestion minimization

One of the main goals in transportation planning is to achieve solutions for two classical problems, the traffic assignment and toll pricing problems. The traffic assignment problem aims to minimize total travel delay among all travelers. Based on data derived from the first problem, the toll pricing problem determines the set of tolls and corresponding tariffs that would collectively benefit all travelers and would lead to a user equilibrium solution. Obtaining high-quality solutions for this framework is a challenge for large networks. In this paper, we propose an approach to solve the two problems jointly, making use of a biased random-key genetic algorithm for the optimization of transportation network performance by strategically allocating tolls on some of the links of the road network. Since a transportation network may have thousands of intersections and hundreds of road segments, our algorithm takes advantage of mechanisms for speeding up shortest-path algorithms.

A biased random-key genetic algorithm for OSPF and DEFT routing to minimize network congestion

Interior gateway routing protocols like OSPF (Open Shortest Path First) and DEFT (Distributed Exponentially-Weighted Flow Splitting) send flow through forward links towards the destination node. OSPF routes only on shortest-weight paths, whereas DEFT sends flow on all forward links, but with an exponential penalty on longer paths. Finding suitable weights for these protocols is known as the weight setting problem. In this paper, we present a biased random-key genetic algorithm for the weight setting prob- lem using both protocols. The algorithm uses dynamic flow and dynamic shortest path computations. We report computational experiments that show that DEFT achieves less network congestion when compared with OSPF, while, however, yielding larger delays.

Genetic algorithms for the no-wait flowshop sequencing problem with time restrictions

This article deals with the no-wait flowshop problem with sequence dependent set-ups and ready times solved by an evolutionary approach. The hybrid genetic algorithm presented here addresses a new hierarchically organized complete ternary tree to represent the population that put together with a recombination plan resembles a parallel processing scheme for solving combinatorial optimization problems. Embedded in the hybrid approach, a novel recursive local search scheme, recursive arc insertion (RAI), is also proposed. The effectiveness of the local search phase is crucial given that it is responsible for about 90% of the total processing time of the algorithm. Instances with known optimal solution are used to test the new algorithm and compare it to a previously proposed heuristic approach.

Estimating clustering indexes in data streams

We present random sampling algorithms that with probability at least 1 - δ compute a (1 ± Ɛ)-approximation of the clustering coefficient and of the number of bipartite clique subgraphs of a graph given as an incidence stream of edges. The space used by our algorithm to estimate the clustering coefficient is inversely related to the clustering coefficient of the network itself. The space used by our algorithm to compute the number K3,3 of bipartite cliques is proportional to the ratio between the number of K1,3 and K3,3 in the graph. Since the space complexity depends only on the structure of the input graph and not on the number of nodes, our algorithms scale very well with increasing graph size. Therefore they provide a basic tool to analyze the structure of dense clusters in large graphs and have many applications in the discovery of web communities, the analysis of the structure of large social networks and the probing of frequent patterns in large graphs. We implemented both algorithms and evaluated their performance on networks from different application domains and of different size; The largest instance is a webgraph consisting of more than 135 million nodes and 1 billion edges. Both algorithms compute accurate results in reasonable time on the tested instances.