Alberto Marchetti-Spaccamela

Bio: Alberto Marchetti-Spaccamela is an academic researcher from Sapienza University of Rome. The author has contributed to research in topics: Approximation algorithm & Scheduling (computing). The author has an hindex of 39, co-authored 178 publications receiving 7108 citations. Previous affiliations of Alberto Marchetti-Spaccamela include Tel Aviv University & French Institute for Research in Computer Science and Automation.

Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties

Abstract: This book documents the state of the art in combinatorial optimization, presenting approximate solutions of virtually all relevant classes of NP-hard optimization problems. The wealth of problems, algorithms, results, and techniques make it an indispensible source of reference for professionals. The text smoothly integrates numerous illustrations, examples, and exercises.

Counting triangles in data streams

Abstract: 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).

The Preemptive Uniprocessor Scheduling of Mixed-Criticality Implicit-Deadline Sporadic Task Systems

Abstract: Systems in many safety-critical application domains are subject to certification requirements. For any given system, however, it may be the case that only a subset of its functionality is safety-critical and hence subject to certification, the rest of the functionality is non safety critical and does not need to be certified, or is certified to a lower level of assurance. An algorithm called EDF-VD (for Earliest Deadline First with Virtual Deadlines) is described for the scheduling of such mixed-criticality task systems. Analyses of EDF-VD significantly superior to previously-known ones are presented, based on metrics such as processor speedup factor (EDF-VD is proved to be optimal with respect to this metric) and utilization bounds.

Multiprocessor Scheduling with Rejection

Abstract: We consider a version of multiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty. An instance of the problem is given by $m$ identical parallel machines and a set of $n$ jobs, with each job characterized by a processing time and a penalty. In the on-line version the jobs become available one by one and we have to schedule or reject a job before we have any information about future jobs. The objective is to minimize the makespan of the schedule for accepted jobs plus the sum of the penalties of rejected jobs. The main result is a $1+\phi\approx 2.618$ competitive algorithm for the on-line version of the problem, where $\phi$ is the golden ratio. A matching lower bound shows that this is the best possible algorithm working for all $m$. For fixed $m$ we give improved bounds; in particular, for $m=2$ we give a $\phi\approx 1.618$ competitive algorithm, which is best possible. For the off-line problem we present a fully polynomial approximation scheme for fixed $m$ and a polynomial approximation scheme for arbitrary $m$. Moreover, we present an approximation algorithm which runs in time $O(n\log n)$ for arbitrary $m$ and guarantees a $2-\frac{1}{m}$ approximation ratio.

Efficient Graph-Based Image Segmentation

Abstract: This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm runs in time nearly linear in the number of graph edges and is also fast in practice. An important characteristic of the method is its ability to preserve detail in low-variability image regions while ignoring detail in high-variability regions.

The knowledge complexity of interactive proof-systems

Abstract: Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

Digraphs Theory Algorithms And Applications

Abstract: The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Proof verification and the hardness of approximation problems

Abstract: We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probability 1 (i.e., for every choice of its random string). For strings not in the language, the verifier rejects every provided “proof” with probability at least 1/2. Our result builds upon and improves a recent result of Arora and Safra [1998] whose verifiers examine a nonconstant number of bits in the proof (though this number is a very slowly growing function of the input length).As a consequence, we prove that no MAX SNP-hard problem has a polynomial time approximation scheme, unless NP = P. The class MAX SNP was defined by Papadimitriou and Yannakakis [1991] and hard problems for this class include vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige et al. [1996] and Arora and Safra [1998] and show that there exists a positive e such that approximating the maximum clique size in an N-vertex graph to within a factor of Ne is NP-hard.