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Publications (20)
Difficulty constitutes a key component of games. It both serves as motivation to play the game and as a way to control progression. Usually, a video game offers a gradual progression in gameplay difficulty, starting with easy levels that allow players to grasp the basic mechanics, and incrementally introducing more challenging obstacles as they pro...
This paper addresses a generalization of polyominoes called ( a , b )- connected discrete figures , where a and b represent the connectivity of the foreground ( i.e. black pixels ) and background ( i.e. white pixels ), respectively. Formally, a finite set of pixels P is ( a , b )-connected if P is a -connected and P is b -connected. By adapting a c...
This paper deals with a generalization of polyominoes called (a, b)-connected discrete figures, where a and b respectively denotes the connectivity of the foreground (i.e. black pixels) and background (i.e. white pixels). Formally, a finite set of pixels P is (a, b)-connected if P is a-connected and P̄ is b-connected. By adapting a combinatorial st...
Explainability is the process of linking part of the inputs given to a calculation to its output, in such a way that the selected inputs somehow “cause” the result. We establish the formal foundations of a notion of explainability for arbitrary abstract functions manipulating nested data structures. We then establish explanation relationships for a...
Robotic Process Automation (RPA) is used in various fields of human activity in order to implement faster and more secure processes through a reduction in the risks or errors but also an increase in the productivity rates. The increase of its use and importance calls for evermore efficient solution methods for this problem. In this paper, the RPA i...
Robotic Process Automation (RPA) is used in various fields of human activity in order to implement faster and more secure processes through a reduction in the risks or errors but also an increase in the productivity rates. The increase of its use and importance calls for evermore efficient solution methods for this problem. In this paper, the RPA i...
Robotic process automation (RPA) helps companies reduce the time required to process tasks by using software or robots to mimic human actions on graphic interfaces. In this
paper, the RPA problem is solved for a financial institution. A set of different types of financial transactions are to be processed with different processing times, volumes, ma...
![Figure 9: Control flow graph and spanning tree for a graph in [2] with...](profile/Fabio-Petrillo/publication/339641871/figure/fig3/AS:864845805154305@1583206716898/Control-flow-graph-and-spanning-tree-for-a-graph-in-2-with-c-o-G1-10-47_Q320.jpg)
Reduce and control complexity is an essential practice in software design. Cyclomatic complexity (CC) is one of the most popular software metrics, applied for more than 40 years. Despite CC is an interesting metric to highlight the number of branches in a program, it clearly not sufficient to represent the complexity in a piece of software. In this...
In 2014, it was conjectured that any polyomino can be factorized uniquely as a product of prime polyominoes [7]. In this paper, we present simple tools from words combinatorics and graph topology that seem very useful in solving the conjecture. The main one is called parallelogram network, which is a particular subgraph of \(G(\mathbb {Z}^2)\) indu...
We present linear time and space operations on discrete paths. First, we compute the outer hull of any discrete path. As a consequence, a linear time and space algorithm is obtained for computing the convex hull. Next, we provide a linear algorithm computing the overlay graph of two simple closed paths. From this overlay graph, one can easily compu...
We present here a linear time and space algorithm for computing the outer hull of any discrete path encoded by its Freeman chain code. The basic data structure uses an enriched version of the data structure introduced by Brlek, Koskas and Provençal: using quadtrees for representing points in the discrete plane ℤ×ℤ with neighborhood links, deciding...
Labelle and Lamathe introduced in 2009 a generalization of the standard combinatorial differential species operator D, by giving a combinatorial interpretation to Ω(X,D)F(X)Ω(X,D)F(X), where Ω(X,T)Ω(X,T) and F(X)F(X) are two-sort and one-sort species respectively. One can show that such operators can be decomposed as sums of products of simpler ope...
Discrete figures (or polyominoes) are fundamental objects in combinatorics and discrete geometry, having been studied in many contexts, ranging from game theory to tiling problems. In 2008, Provençal introduced the concept of prime and composed polyominoes, which arises naturally from a composition operator acting on these discrete figures. Our goa...
