# Gianluca Cincotti's research while affiliated with University of Catania and other places

## Publications (11)

Article
This paper enriches a pre-existing decision algorithm, which in turn augmented a fragment of Tarski's elementary algebra with one-argument real functions endowed with a continuous first derivative. In its present (still quantifier-free) version, our decidable language embodies the addition of functions and multiplication of functions by scalars; th...
Article
In this paper we address the decision problem for a fragment of unquantified formulae of real analysis, which, besides the operators of Tarski’s theory of reals, includes also strict and non-strict predicates expressing comparison, monotonicity, concavity, and convexity of continuous real functions over possibly unbounded intervals.The decision res...
Article
We propose a simple and natural linear randomized algorithm for the approximate 1-median selection problem in metric spaces. The 1-median of a finite subset S of a metric space is the element of S which minimizes the average distance from the remaining points in S. This problem is extremely important in most applications using clustering of metric...
Article
We present an efficient and practical algorithm for the internal sorting problem. Our algorithm works in-place and, on the average, has a running-time of in the size n of the input. More specifically, the algorithm performs comparisons and element moves on the average. An experimental comparison of our proposed algorithm with the most efficient var...
Article
We address the decision problem for an unquantied fragment of graph theory in presence of constructs related to the reachability notion, both in the undirected and directed case. Besides individual, set, and graph variables, the language studied includes basic boolean set operators and predicates (such as [, , n, 2, , =, and nite enumerations) | ap...
Article
In this paper we consider the decidability of a fragment of analysis theory taking into account continuous and differentiable (with continuous derivative) real functions. In particular, such theory, denoted with RDF, includes predicates treating comparisons, monotonicity, convexity and derivative of functions over bounded closed or unbounded interv...
Article
The decidability of RMCF + , a fragment of analysis including functional predicates for comparisons, monotonicity , strict monotonicity, concavity or convexity, strict concavity or convexity, is reported. Such functional predicates referred to properties of continuous functions over bounded closed or unbounded intervals. The decision algorithm is o...
Conference Paper
Full-text available
We present an efficient algorithm for the approximate median selection problem. The algorithm works in-place; it is fast and easy to implement. For a large array it returns, with high probability, a very close estimate of the true median. The running time is linear in the length n of the input. The algorithm performs fewer than $$\frac{4} {3}n$$...
Conference Paper
We present a practically efficient algorithm for the internal sorting problem. Our algorithm works in-place and, on the average, has a running-time of O(n log n) in the length n of the input. More specifically, the algorithm performs n log n + 3n comparisons and n log n + 2.65n element moves on the average. An experimental comparison of our propos...
Article
Full-text available
We present an efficient algorithm for the approximate median selection problem. The algorithm works in-place
Article
Full-text available
We present an efficient randomized algorithm for the approximate k-th selection problem. It works in-place and it is fast and easy to implement. The running time is linear in the length of the input. For a large input set the algorithm returns, with high probability, an element which is very close to the exact k-th element. The quality of the appro...

## Citations

... c o m / l o c a t e / i n s worst-case) for the median selection problem was due to Bent and John [1] in 1985. Refer to [3,4] for the detailed research on the Selection problem. The SelectSum q Problem is a fundamenta l problem for many practical applications. ...
... Our transfer theorem covers this refined version of QuickMergesort, as well, which had not been analyzed before. 2 The rest of the paper is structured as follows: In Section 2, we summarize previous work on QuickXsort with a focus on contributions to its analysis. Section 3 collects mathematical facts and notations used later. ...
... This new upper bound also allows us to strengthen Iwama and Teruyama's bound for their combined algorithm to n lg n − 1.4112n. [3] were the first to explicitly give a name to the mixture of Quicksort with another sorting method; they proposed QuickHeapsort. However, the concept of QuickXsort (without calling it like that) was first used in UltimateHeapsort by Katajainen [28]. ...
... Chen and Dumitrescu [6] propose RepeatedStep (discussed in detail in §3), a variant of MedianOfMedians that groups 3 or 4 elements (the original uses groups of 5 or more elements) and prove its linearity. Battiato et al. [2] describe Sicilian Median Selection, an algorithm for computing an approximate median that may be considered the transitive closure of RepeatedStep. ...
... The result is obtained through reduction to the decidability problem for two-level syllogistic, which by itself is NP-complete. Another paper in this context is [19]. In this case the authors address the decision problem for a fragment of real analysis, consisting of unquantified formulae which, in addition to the operators of Tarski's theory of reals, involve predicates of comparison, monotonicity, concavity, and convexity of continuous real functions, over possibly unbounded intervals. ...
... Median computation is one of the fundamental ways of finding central vertices of the graph, with huge impact on practical research [5,6,25,27,37,41]. A significant amount of research has been devoted to efficient algorithms for finding medians of networks [34,39,40] or approximating the notion [13,14]. We note the seminal work of Indyk [28] which includes 1 + ε approximation to 1-median in time O(n/ε 5 ) in metric spaces -we note that the form of approximation there differs from ours, although the very-high level technique of using random sampling is common. ...
... is not too close to either extreme. In particular, (i, j)-mediocre elements where i = n−1 2 , j = n 2 (and symmetrically exchanged), are medians of S. Previous work on approximate selection (in this sense) includes [5,17]. ...
... Cantone and Cutello's language does not deal with reachability and acyclicity. Cantone and Cincotti [4] studied the decision problem for the language UGRA (undirected graphs with reachability and acyclicity). Intuitively, UGRA is the same as DGRA, except that it deals with undirected graphs. ...