arXiv subjects

Samer Nofal

Publications and source records attributed to Samer Nofal.

2 recordsLinked to original sources

arXiv2021

On Computing Stable Extensions of Abstract Argumentation Frameworks

An \textit{abstract argumentation framework} ({\sc af} for short) is a directed graph $(A,R)$ where $A$ is a set of \textit{abstract arguments} and $R\subseteq A \times A$ is the \textit{attack} relation. Let $H=(A,R)$ be an {\sc af}, $S \subseteq A$ be a set of arguments and $S^+ = \{y \mid \exists x\in S \text{ with }(x,y)\in R\}$. Then, $S$ is a \textit{stable extension} in $H$ if and only if $S^+ = A\setminus S$. In this paper, we present a thorough, formal validation of a known backtracking algorithm for listing all stable extensions in a given {\sc af}.

cs.DS↗

arXiv2021

A Smart Backtracking Algorithm for Computing Set Partitions with Parts of Certain Sizes

Let $α=\{a_1,a_2,a_3,...,a_n\}$ be a set of elements, $δ< n$ be a non-negative integer, and $Γ: α\to \{0, 1, 2, ..., n\}$ be a total mapping. Then, we call $Γ$ a \emph{partition} of $α$ if and only if for all $x \in α$, $Γ(x) \neq 0$. Further, we call $Γ$ a $δ$-\emph{partition} of $α$ if and only if $Γ$ is a partition of $α$ and for all $i \in \{1, 2, 3, ..., n\}$, $|\{x: Γ(x)=i\}| > δ$. We give a non-trivial algorithm that computes all $δ$-partitions of $α$ in $Ω(n)$ time. On the opposite, a naive generate-and-test algorithm would compute all $δ$-partitions of $α$ in $Ω(nB_n)$ time where $B_n$ is the Bell number.

cs.DS↗