Umberto Nanni

Fully Dynamic Algorithms for Maintaining Shortest Paths Trees

We propose fully dynamic algorithms for maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling insertions, deletions, and weight updates of edges. The algorithms require linear space and optimal query time. The cost of the update operations depends on the class of the considered graph and on the number of the output updates, i.e., on the number of vertices that, due to an edge modification, either change the distance from the source or change the parent in the shortest paths tree. We first show that, if we deal only with updates on the weights of edges, then the update procedures require O(logn) worst case time per output update for several classes of graphs, as in the case of graphs with bounded genus, bounded arboricity, bounded degree, bounded treewidth, and bounded pagenumber. For general graphs with n vertices and m edges the algorithms require O(mlogn) worst case time per output update. We also show that, if insertions and deletions of edges are allowed, then similar amortized bounds hold.

Standard Preanalytical Coding for Biospecimens: Defining the Sample PREanalytical Code

Background: Management and traceability of biospecimen preanalytical variations are necessary to provide effective and efficient interconnectivity and interoperability between Biobanks. Methods: Therefore, the International Society for Biological and Environmental Repositories Biospecimen Science Working Group developed a “Standard PREanalytical Code” (SPREC) that identifies the main preanalytical factors of clinical fluid and solid biospecimens and their simple derivatives. Results: The SPREC is easy to implement and can be integrated into Biobank quality management systems and databases. It can also be extended to nonhuman biorepository areas. Its flexibility allows integration of new novel technological developments in future versions. SPREC version 01 is presented in this article. Conclusions and Impact: Implementation of the SPREC is expected to facilitate and consolidate international multicenter biomarker identification research and biospecimen research in the clinical Biobank environment. Cancer Epidemiol Biomarkers Prev; 19(4); 1004–11. ©2010 AACR.

Standard preanalytical coding for biospecimens: review and implementation of the Sample PREanalytical Code (SPREC).

The first version of the Standard PREanalytical Code (SPREC) was developed in 2009 by the International Society for Biological and Environmental Repositories (ISBER) Biospecimen Science Working Group to facilitate documentation and communication of the most important preanalytical quality parameters of different types of biospecimens used for research. This same Working Group has now updated the SPREC to version 2.0, presented here, so that it contains more options to allow for recent technological developments. Existing elements have been fine tuned. An interface to the Biospecimen Reporting for Improved Study Quality (BRISQ) has been defined, and informatics solutions for SPREC implementation have been developed. A glossary with SPREC-related definitions has also been added.

Semidynamic Algorithms for Maintaining Single-Source Shortest Path Trees

Abstract. We consider the problem of updating a single-source shortest path in either a directed or an undirected graph, with positive real edge weights. Our algorithms for the incremental problem (handling edge insertions and cost decrements) work for any graph; they have optimal space requirements and query time, but their performances depend on the class of the considered graph. The cost of updates is computed in terms of amortized complexity and depends on the size of the output modifications. In the case of graphs with bounded genus (including planar graphs), graphs with bounded arboricity (including bounded degree graphs), and graphs with bounded treewidth, the incremental algorithms require O(log n) amortized time per vertex update, where a vertex is considered updated if it reduces its distance from the source. For general graphs with n vertices and m edges our incremental solution requires O( \sqrt{m} log n) amortized time per vertex update. We also consider the decremental problem for planar graphs, providing algorithms and data structures with analogous performances. The algorithms, based on Dijkstras technique [6], require simple data structures that are really suitable for a practical and straightforward implementation.

Maintaining a topological order under edge insertions

Abstract A topological order of the vertices of a directed acyclic graph G = ( V , E ) is any total order ord such that if ( x , y ) ϵ E , then x precedes y in ord . In this paper we consider the dynamic version of this problem, and provide simple algorithms and data structures achieving O( n ) amortized time per edge insertion starting from an empty graph, which favorably compares to the trivial O( m + n ) time bound per operation obtained applying the off-line algorithm. The additional space requirement, beside the representation of the graph itself, is O( n ). Experimental results show that our algorithm performs in practice orders of magnitude faster than the off-line algorithm.

Dynamic maintenance of directed hypergraphs

Abstract In this paper we are concerned with the on-line maintenance of directed hypergraphs, a generalization of directed graphs previously introduced in the literature. In particular, we show how to maintain efficiently information about hyperpaths while new hyperarcs are inserted. We present a data structure which allows us to check whether there exists a hyperpath between an arbitrarily given pair of nodes in constant time and to return such a hyperpath in a time which is linear in its size. The total time required to maintain the data structure during the insertion of new hyperarcs is O( mn ), where m is the total size of the description of the hyperarcs and n is the number of nodes. This generalizes a previous result known for directed graphs and has applications in several areas of computer science, such as rewriting systems, database schemes, logic programming and problem solving. An extension of these results to hyperpaths between sets of nodes is also presented.

A fully dynamic algorithm for distributed shortest paths

We propose a fully dynamic distributed algorithm for the all-pairs shortest paths problem on general networks with positive real edge weights. If Δσ is the number of pairs of nodes changing the distance after a single edge modification σ (insert, delete, weight decrease, or weight increase) then the message complexity of the proposed algorithm is O(nΔσ) in the worst case, where n is the number of nodes of the network. If Δσ = o(n2), this is better than recomputing everything from scratch after each edge modification. Up to now only a result of Ramarao and Venkatesan was known, stating that the problem of updating shortest paths in a dynamic distributed environment is as hard as that of computing shortest paths.

Fully Dynamic Shortest Paths and Negative Cycles Detection on Digraphs with Arbitrary Arc Weights

We study the problem of maintaining the distances and the shortest paths from a source node in a directed graph with arbitrary arc weights, when weight updates of arcs are performed. We propose algorithms that work for any graph and require linear space and optimal query time. If a negative{length cycle is added during weight-decrease operations it is detected by the algorithms. The algorithms explicitly deal with zero{length cycles. We show that, if the graph has a k-bounded accounting function (as in the case of graphs with genus, arboricity, degree, treewidth or pagenumber bounded by k, and k-inductive graphs) the algorithms require O(k ċ n ċ log n) worst case time. In the case of graphs with n nodes and m arcs k = O(√m); this gives O(√m ċ n ċ log n) worst case time per operation, which is better for a factor of O(√m log n) than recomputing everything from scratch after each update. If we perform also insertions and deletions of arcs, then the above bounds become amortized.

On-line Graph Algorithms for Incremental Compilation

Compilers usually construct various data structures which often vary only slightly from compilation run to compilation run. This paper describes in a compact and uniform way solutions to several problems arising in order to quickly update these data structures instead of building them from scratch each time. All the considered problems can be reduced to graph problems. Specifically, we give algorithms for the dynamic problems of loop detection, topological order, reachability from the start routine, and transitive closure.

Maintaining Shortest Paths in Digraphs with Arbitrary Arc Weights: An Experimental Study

We present the first experimental study of the fully dynamic single-source shortest paths problem in digraphs with arbitrary (negative and non-negative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus a new algorithm devised to be as simple as possible while matching the best worst-case bounds for the problem. According to experiments performed on randomly generated test sets, all the considered dynamic algorithms are faster by several orders of magnitude than recomputing from scratch with the best static algorithm. The experiments also reveal that, although the simple dynamic algorithm we suggest is usually the fastest in practice, other dynamic algorithms proposed in the literature yield better results for specific kinds of test sets.