Marking problem: a new approach to reachability assurance in digraphs

Abstract

Abstract. Let G be a weighted digraph and s and t be two vertices of G. The reachability assurance (RA) problem is how to label the edges of G such that every path starting at s finally reaches t and the sum of the weights of the labeled edges, called the RA cost, is minimal. The common approach to the RA problem is pathfinding, in which a path is sought from s to t and then the edges of the path are labeled. This paper introduces a new approach, the marking problem (MP), to the RA problem. Compared to the common pathfinding approach, the proposed MP approach has a lower RA cost. It is shown that the MP is NP-complete, even when the underlying digraph is an unweighted directed acyclic graph (DAG) or a weighted DAG with an out-degree of two. An appropriate heuristic algorithm to solve the MP in polynomial time is provided. To mitigate the RA problem as a serious challenge in this area, application of the MP in software testing is also presented. By evaluating the datasets from various program flow graphs, it is shown that the MP is superior to the pathfinding in the context of test case generation.

Logical s-t Min-Cut Problem: An Extension to the Classic s-t Min-Cut Problem

“…the labels of a set of edges of G. As G indicates the flow graph of a computer program, making False the label of an edge e of G is equivalent to the removal of e from G. Also, according to the semantic of a computer program, we cannot remove (make False the labels of) all outgoing edges of a vertex of G together, implying that the removal should be logical. Therefore, the problem A can be rephrased as the following problem called OP T R (Optimal Reach) [10].…”

“…We demonstrate the LST M C problem cannot be approximated within αlogn for some constant α. Let OP T R be the following problem: how to remove some edges of G where all paths starting from s pass through t and the removal is both minimal and logical [10]. We show that both problems of LST M C and OP T R are reducible to each other.…”

Constructing Automated Test Oracle for Low Observable Software

“…The input values should satisfy some testing criteria such that the testers have a dependable estimation of the program reliability [1]. To reduce laboriousness, inaccuracy, and intolerable costs of manual test data generation, a signi cant amount of research has been dedicated to automating the process of test data generation [2,3].…”