TY - JOUR
T1 - Logical s-t Min-Cut Problem: An Extension to the Classic s-t Min-Cut Problem
TT -
JF - IJMSI
JO - IJMSI
VL - 17
IS - 2
UR - http://ijmsi.ir/article-1-1481-en.html
Y1 - 2022
SP - 253
EP - 271
KW - Logical s-t min-cut
KW - LSTMC
KW - Complexity
KW - Inapproximability
KW - Flow graph
KW - Test case generation.
N2 - 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.
M3 10.52547/ijmsi.17.2.253
ER -