Giorgio Gambosi – författare

The papers in this volume were presented at the Fourth Italian Conference on Algorithms and Complexity (CIAC 2000). The conference took place on March 1-3, 2000, in Rome (Italy), at the conference center of the University of Rome \La Sapienza". This conference was born in 1990 as a national meeting to be held every three years for Italian researchers in algorithms, data structures, complexity, and parallel and distributed computing. Due to a signi cant participation of foreign reaserchers, starting from the second conference, CIAC evolved into an international conference. In response to the call for papers for CIAC 2000, there were 41 subm- sions, from which the program committee selected 21 papers for presentation at the conference. Each paper was evaluated by at least three program committee members. In addition to the selected papers, the organizing committee invited Giorgio Ausiello, Narsingh Deo, Walter Ruzzo, and Shmuel Zaks to give plenary lectures at the conference. We wish to express our appreciation to all the authors of the submitted papers, to the program committee members and the referees, to the organizing committee, and to the plenary lecturers who accepted our invitation.

N COMPUTER applications we are used to live with approximation. Var­ I ious notions of approximation appear, in fact, in many circumstances. One notable example is the type of approximation that arises in numer­ ical analysis or in computational geometry from the fact that we cannot perform computations with arbitrary precision and we have to truncate the representation of real numbers. In other cases, we use to approximate com­ plex mathematical objects by simpler ones: for example, we sometimes represent non-linear functions by means of piecewise linear ones. The need to solve difficult optimization problems is another reason that forces us to deal with approximation. In particular, when a problem is computationally hard (i. e. , the only way we know to solve it is by making use of an algorithm that runs in exponential time), it may be practically unfeasible to try to compute the exact solution, because it might require months or years of machine time, even with the help of powerful parallel computers. In such cases, we may decide to restrict ourselves to compute a solution that, though not being an optimal one, nevertheless is close to the optimum and may be determined in polynomial time. We call this type of solution an approximate solution and the corresponding algorithm a polynomial-time approximation algorithm. Most combinatorial optimization problems of great practical relevance are, indeed, computationally intractable in the above sense. In formal terms, they are classified as Np-hard optimization problems.

The papers in this volume were presented at the Fourth Italian Conference on Algorithms and Complexity (CIAC 2000). The conference took place on March 1-3, 2000, in Rome (Italy), at the conference center of the University of Rome \La Sapienza". This conference was born in 1990 as a national meeting to be held every three years for Italian researchers in algorithms, data structures, complexity, and parallel and distributed computing. Due to a signi cant participation of foreign reaserchers, starting from the second conference, CIAC evolved into an international conference. In response to the call for papers for CIAC 2000, there were 41 subm- sions, from which the program committee selected 21 papers for presentation at the conference. Each paper was evaluated by at least three program committee members. In addition to the selected papers, the organizing committee invited Giorgio Ausiello, Narsingh Deo, Walter Ruzzo, and Shmuel Zaks to give plenary lectures at the conference. We wish to express our appreciation to all the authors of the submitted papers, to the program committee members and the referees, to the organizing committee, and to the plenary lecturers who accepted our invitation.

N COMPUTER applications we are used to live with approximation. Var­ I ious notions of approximation appear, in fact, in many circumstances. One notable example is the type of approximation that arises in numer­ ical analysis or in computational geometry from the fact that we cannot perform computations with arbitrary precision and we have to truncate the representation of real numbers. In other cases, we use to approximate com­ plex mathematical objects by simpler ones: for example, we sometimes represent non-linear functions by means of piecewise linear ones. The need to solve difficult optimization problems is another reason that forces us to deal with approximation. In particular, when a problem is computationally hard (i. e. , the only way we know to solve it is by making use of an algorithm that runs in exponential time), it may be practically unfeasible to try to compute the exact solution, because it might require months or years of machine time, even with the help of powerful parallel computers. In such cases, we may decide to restrict ourselves to compute a solution that, though not being an optimal one, nevertheless is close to the optimum and may be determined in polynomial time. We call this type of solution an approximate solution and the corresponding algorithm a polynomial-time approximation algorithm. Most combinatorial optimization problems of great practical relevance are, indeed, computationally intractable in the above sense. In formal terms, they are classified as Np-hard optimization problems.

N COMPUTER applications we are used to live with approximation. Var­ I ious notions of approximation appear, in fact, in many circumstances. One notable example is the type of approximation that arises in numer­ ical analysis or in computational geometry from the fact that we cannot perform computations with arbitrary precision and we have to truncate the representation of real numbers. In other cases, we use to approximate com­ plex mathematical objects by simpler ones: for example, we sometimes represent non-linear functions by means of piecewise linear ones. The need to solve difficult optimization problems is another reason that forces us to deal with approximation. In particular, when a problem is computationally hard (i. e. , the only way we know to solve it is by making use of an algorithm that runs in exponential time), it may be practically unfeasible to try to compute the exact solution, because it might require months or years of machine time, even with the help of powerful parallel computers. In such cases, we may decide to restrict ourselves to compute a solution that, though not being an optimal one, nevertheless is close to the optimum and may be determined in polynomial time. We call this type of solution an approximate solution and the corresponding algorithm a polynomial-time approximation algorithm. Most combinatorial optimization problems of great practical relevance are, indeed, computationally intractable in the above sense. In formal terms, they are classified as Np-hard optimization problems.