By David Peleg (auth.), Rossella Petreschi, Giuseppe Persiano, Riccardo Silvestri (eds.)
This publication constitutes the refereed lawsuits of the fifth Italian convention on Algorithms and Computation, CIAC 2003, held in Rome, Italy in might 2003.
The 23 revised complete papers awarded have been rigorously reviewed and chosen from fifty seven submissions. one of the subject matters addressed are complexity, complexity idea, geometric computing, matching, on-line algorithms, combinatorial optimization, computational graph idea, approximation algorithms, community algorithms, routing, and scheduling.
Read Online or Download Algorithms and Complexity: 5th Italian Conference, CIAC 2003, Rome, Italy, May 28–30, 2003. Proceedings PDF
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Extra info for Algorithms and Complexity: 5th Italian Conference, CIAC 2003, Rome, Italy, May 28–30, 2003. Proceedings
The reduction follows the one in section 2 using modiﬁed literal and variable patterns, as shown in ﬁgure 5. It is not hard to check that the properties mentioned in Theorem 1 hold here as well. e. 1 for the vertex-guard problems and the one used in Proposition 1 (with the modiﬁed literal and variable patterns) for the edge-guard problems. All the reductions are from Max-5-occurrence-3-Sat to the problem in hand. e. “overseeing a part of it” instead of “overseeing all of it”. Proposition 2. The watching versions of Maximum Value Vertex Guard and Maximum Value Edge Guard problems are APX-hard.
We assign value 8δn to every other segment. The properties of Theorem 1 hold (details are omitted for brevity). Consider now the following problem: Deﬁnition 3. Given is a polygon P without holes and an integer k > 0. Let L(b) be the euclidean length of the line segment b. The Maximum Length Vertex/Edge Guard problem asks to place k vertex (edge) guards so that the euclidean length of the overseen part of P ’s boundary is maximum. Proposition 3. Maximum Length Vertex/Edge Guard is APX-hard. Proof.
4, pp. 412-458, 1998. 2. P. K. Agarwal, B. Aronov, M. Sharir and S. Suri, Selecting Distances in the Plane, Algorithmica, vol. 9, pp. 495-514, 1993. 3. T. Akutsu, H. Tamaki, and T. Tokuyama, Distribution of Distances and Triangles in a Plane Set and Algorithms for Computing the Largest Common Point Sets, Discrete Computational Geometry, vol. 20, pp. 307-331, 1998. 4. H. Alt and L. J. Guibas, Discrete Geometric Shapes: Matching, Interpolation, and Approximation - A Survey, Technical Report B 96-11, Freie Universit¨ at Berlin, 1996.