By Giorgio Ausiello, Stefano Leonardi, Alberto Marchetti-Spaccamela (auth.), Giancarlo Bongiovanni, Rossella Petreschi, Giorgio Gambosi (eds.)

The papers during this quantity have been offered on the Fourth Italian convention on Algorithms and Complexity (CIAC 2000). The convention happened on March 1-3, 2000, in Rome (Italy), on the convention heart of the collage of Rome \La Sapienza". This convention used to be born in 1990 as a countrywide assembly to be held each 3 years for Italian researchers in algorithms, information buildings, complexity, and parallel and allotted computing. as a result of a signi cant participation of overseas reaserchers, ranging from the second one convention, CIAC developed into a world convention. in accordance with the decision for papers for CIAC 2000, there have been forty-one subm- sions, from which this system committee chosen 21 papers for presentation on the convention. each one paper used to be evaluated via at the very least 3 application committee contributors. as well as the chosen papers, the organizing committee invited Giorgio Ausiello, Narsingh Deo, Walter Ruzzo, and Shmuel Zaks to provide plenary lectures on the convention. we want to exhibit our appreciation to all of the authors of the submitted papers, to this system committee individuals and the referees, to the organizing committee, and to the plenary teachers who approved our invitation.

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Extra info for Algorithms and Complexity: 4th Italian Conference, CIAC 2000 Rome, Italy, March 1–3, 2000 Proceedings

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2 Introduction to the Solution Space Before explaining the development of the algorithms, it is helpful to gain some intuition about the solution space. Given that the data is both noisy and incomplete, the problem can be under-constrained and/or over-constrained. In this domain, a “constraint” refers to a measurement between two probes (since it constrains the placement of the probes). An under-constrained problem instance is one in which a probe might not have enough measurements to other probes to uniquely determine its position.

The replacement edge will be the smallest-weight edge (a, b) which (1) guarantees that the new edge does not increase the diameter, and (2) guarantees reducing the length of a longest path in the tree at least by one. We enforce condition (1) by: 26 Narsingh Deo and Ayman Abdalla eccsubtree1(a) ≤ eccsubtree1(x) AND eccsubtree2(b) ≤ eccsubtree2(y) , (1) and condition (2) by: eccsubtree1(a) < eccsubtree1(x) OR eccsubtree2(b) < eccsubtree2(y) . (2) If no such edge (a, b) is found, we must remove an edge farther from the center of the tree, instead.

Therefore, the DCMST for this type of graphs will lose less low-weight edges than in unrestricted random graphs. 120 Time (seconds) 100 80 ERM1 60 ERM2 40 20 0 100 200 300 400 500 Number on Nodes (n) weight ratio: DCMST / MST Fig. 7. Time to reduce diameter from n−1 to 10 using two different edge-replacement methods 10 8 DCMST(3) 6 DCMST(10) 4 DCMST(4) 2 0 100 200 300 400 500 1000 Number of Nodes (n) Fig. 8. Quality of DCMST(4) and DCMST(10) for unrestricted random graphs Furthermore, the weight of DCMST(4) was lower than that of DCMST(10) in unrestricted random graphs.

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