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By Kurt Mehlhorn (auth.), Tiziana Calamoneri, Irene Finocchi, Giuseppe F. Italiano (eds.)

This publication constitutes the refereed complaints of the sixth Italian convention on Algorithms and Computation, CIAC 2006, held in Rome, Italy, in could 2006.

The 33 revised complete papers offered including three invited papers have been rigorously reviewed and chosen from eighty submissions. one of the themes addressed are sequential, parallel and dispensed algorithms, info constructions, approximation algorithms, randomized algorithms, online algorithms, graph algorithms, research of algorithms, set of rules engineering, algorithmic video game conception, computational biology, computational complexity, verbal exchange networks, computational geometry, cryptography, discrete optimization, graph drawing, mathematical programming, and quantum algorithms.

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Extra resources for Algorithms and Complexity: 6th Italian Conference, CIAC 2006, Rome, Italy, May 29-31, 2006. Proceedings

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A fractional optimal solution is x∗ (S) = (k + 1)/(2k) for each line S and y ∗ (S, u) = 1/2 for every line S and rectangle u. This means that the value of the fractional minimum is 1 + k1 , while the integral optimum is 2. The following definitions apply to both lp-hard and lp-soft. We refer to a pair (x, y) as a partial cover if it satisfies all the constraints, except (perhaps) constraints of type (1). A rectangle is covered if its type (1) constraint is satisfied. Approximation Algorithms for Capacitated Rectangle Stabbing 23 If S | u∈S y(S, u) ≥ α, we refer to u as α-covered.

An 8-approximation algorithm for the one dimensional case is also presented. In the full paper, we present two hardness results. The first mimics the hardness result given in [2] to show that weighted hard-2rs is set-cover-hard, even if all weights are in {0, 1}. The second result proves that it is NP-hard to approximate drs with a ratio of c · log d, for some constant c. Note that the dimension d is considered here to be part of the input. 2 Interval Stabbing with Soft Capacities In this section we present a 2-approximation algorithm for soft-1rs.

6 Interval Stabbing with Hard Capacities In this section we present an 8-approximation algorithm for hard-1rs. The algorithm augments the positive cover obtained by Claim 3 with ε = 1/4. A local greedy rule is used to select the line to be added to the partial cover. 1 Thirsty Lines and Dams Throughout this section we consider a partial cover (x, y) such that x is integral and y is maximum with respect to x. Definition 5. Let (x, y) be a partial cover such that x is integral and y is maximum with respect to x.

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