Camil Demetrescu

Dynamic graph algorithms

In dynamic graph algorithms the following provide-or-boundproblem has to be solved quickly: Given a set S containing a subset R and a way of generating random elements fromS testing for membership inR, either (i) provide an element of R or (ii) give a (small) upper bound on the size of R that holds with high probability. We give an optimal algorithm for this problem. This algorithm improves the time per operation for various dyamic graph algorithms by a factor ofO(logn). For example, it improves the time per update for fully dynamic connectivity fromO(log n) toO(log n).

Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier

We introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive closure, in particular we devise a deterministic algorithm for general directed graphs that achieves O(n/sup 2/) amortized time for updates, while preserving unit worst-case cost for queries. In case of deletions only, our algorithm performs updates faster in O(n) amortized time. Our matrix-based approach yields an algorithm for directed acyclic graphs which breaks through the O(n/sup 2/) barrier on the single-operation complexity of fully dynamic transitive closure. We can answer queries in O(n/sup /spl epsiv//) time and perform updates in O(n/sup /spl omega/(1,/spl epsiv/,1)-/spl epsiv//+n/sup 1+/spl epsiv//) time, for any /spl epsiv//spl isin/[0,1], where /spl omega/(1,/spl epsiv/,1) is the exponent of the multiplication of an n/spl times/n/sup /spl epsiv// matrix by an n/sup /spl epsiv///spl times/n matrix. The current best bounds on /spl omega/(1,/spl epsiv/,1) imply an O(n/sup 0.575/) query time and an O(n/sup 1.575/) update time. Our subquadratic algorithm is randomized, and has one-side error.

Reversible Execution and Visualization of Programs with LEONARDO

In this paper we present LEONARDO, an integrated environment for software visualization that allows the user to edit, compile, execute, and animate general-purpose C programs. LEONARDO relies on a logic-based approach to visualization: a mapping between concrete and abstract data structures can be declared through a logic visualization language and animations are conceived as reflecting formal properties of algorithms. LEONARDO is able to automatically detect visual events during the execution of programs and simplifies the creation of visualizations according to an incremental approach. Moreover, it guarantees the complete reversibility of computations, bounded only by the potentiality of the working machine, and appears simple to be used. The latest version of LEONARDO is currently available over the Internet at the URLhttp: //www.dis.uniroma1.it/~demetres/Leonardo/.

A new approach to dynamic all pairs shortest paths

We study novel combinatorial properties of graphs that allow us to devise a completely new approach to dynamic all pairs shortest paths problems. Our approach yields a fully dynamic algorithm for general directed graphs with non-negative real-valued edge weights that supports any sequence of operations in Õ(n2) amortized time per update and unit worst-case time per distance query, where n is the number of vertices. We can also report shortest paths in optimal worst-case time. These bounds improve substantially over previous results and solve a long-standing open problem. Our algorithm is deterministic and uses simple data structures.

Oracles for Distances Avoiding a Failed Node or Link

We consider the problem of preprocessing an edge-weighted directed graph

Input-sensitive profiling

G

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

to answer queries that ask for the length and first hop of a shortest path from any given vertex

Dynamic shortest paths and transitive closure: Algorithmic techniques and data structures ✩

x

Specifying Algorithm Visualizations: Interesting Events or State Mapping?

to any given vertex

Trade-offs for fully dynamic transitive closure on DAGs: breaking through the O ( n 2 barrier

y