%0 Journal Article
%A Valizadeh, M.
%A Tadayon, M. H.
%T Logical s-t Min-Cut Problem: An Extension to the Classic s-t Min-Cut Problem
%J Iranian Journal of Mathematical Sciences and Informatics
%V 17
%N 2
%U http://ijmsi.ir/article-1-1481-en.html
%R 10.52547/ijmsi.17.2.253
%D 2022
%K Logical s-t min-cut, LSTMC, Complexity, Inapproximability, Flow graph, Test case generation.,
%X Let $G$ be a weighted digraph, $s$ and $t$ be two vertices of $G$, and $t$ is reachable from $s$. The logical $s$-$t$ min-cut (LSTMC) problem states how $t$ can be made unreachable from $s$ by removal of some edges of $G$ where (a) the sum of weights of the removed edges is minimum and (b) all outgoing edges of any vertex of $G$ cannot be removed together. If we ignore the second constraint, called the logical removal, the LSTMC problem is transformed to the classic $s$-$t$ min-cut problem. The logical removal constraint applies in situations where non-logical removal is either infeasible or undesired. Although the $s$-$t$ min-cut problem is solvable in polynomial time by the max-flow min-cut theorem, this paper shows the LSTMC problem is NP-Hard, even if $G$ is a DAG with an out-degree of two. Moreover, this paper shows that the LSTMC problem cannot be approximated within $alpha log n$ in a DAG with $n$ vertices for some constant $alpha$. The application of the LSTMC problem is also presented intest case generation of a computer program.
%> http://ijmsi.ir/article-1-1481-en.pdf
%P 253-271
%& 253
%!
%9 Research paper
%L A-10-4287-1
%+ Faculty of Information Technology, Iran Telecommunication Research Center (ITRC), P.O.Box:14155-3961, Tehran, Iran
%G eng
%@ 1735-4463
%[ 2022