Marco Protasi

Bio: Marco Protasi is an academic researcher from University of Rome Tor Vergata. The author has contributed to research in topics: Optimization problem & L-reduction. The author has an hindex of 11, co-authored 38 publications receiving 3056 citations.

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.

Reactive search, a history-sensitive heuristic for MAX-SAT

Abstract: The Reactive Search (RS) method proposes the integration of a simple history-sensitive (machine learning) scheme into local search for the on-line determination of free parameters. In this paper a new RS algorithm is proposed for the approximated solution of the Maximum Satisfiability problem: a component based on local search with temporary prohibitions (Tabu Search) is complemented with a reactive scheme that determines the appropriate value of the prohibition parameter by monitoring the Hamming distance along the search trajectory. The proposed algorithm (H-RTS) can therefore be characterized as a dynamic version of Tabu Search.In addition, the non-oblivious functions recently introduced in the framework of approximation algorithms are used to discover a better local optimum in the initial part of the searchThe algorithm is developed in two phases. First the bias-diversification properties of individual candidate components are analyzed by extensive empirical evaluation, then a reactive scheme is added to the winning component, based on Tabu Search.The final tests on a benchmark of random MAX-3-SAT and MAX-4-SAT problems demonstrate the superiority of H-RTS with respect to alternative heuristics.

Approximate Algorithms and Heuristics for MAX-SAT

Abstract: In the Maximum Satisfiability (MAX-SAT) problem one is given a Boolean formula in conjunctive normal form, i.e., as a conjunction of clauses, each clause being a disjunction. The task is to find an assignment of truth values to the variables that satisfies the maximum number of clauses.

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.

Metaheuristics in combinatorial optimization: Overview and conceptual comparison

Abstract: The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behavior of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

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.