Strengthening a linear reformulation of the 0-1 cubic knapsack problem via variable reordering

Forrester, Richard J.; Waddell, Lucas

doi:10.1007/s10878-021-00840-z

Cited by 2 publications

(1 citation statement)

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“…In the literature, many extensions of the binary knapsack problem have been considered that allow less restrictive types of objectives functions, such as quadratic [14], cubic [15] and submodular [16] objective functions. However, the following theorem shows that objective functions d arising from cd-ATs form the even larger class of nondecreasing functions (i.e., x y implies f (x) ≤ f (y), see Definition 2).…”

Section: Relation To Knapsack Problems and Np-completenessmentioning

confidence: 99%

Cost-Damage Analysis of Attack Trees

Lopuhaä-Zwakenberg,

Stoelinga

2023

2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN)

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Attack trees (ATs) are a widely deployed modelling technique to categorize potential attacks on a system. An attacker of such a system aims at doing as much damage as possible, but might be limited by a cost budget. The maximum possible damage for a given cost budget is an important security metric of a system. In this paper, we find the maximum damage given a cost budget by modelling this problem with ATs, both in deterministic and probabilistic settings. We show that the general problem is NP-complete, and provide heuristics to solve it. For general ATs these are based on integer linear programming. However when the AT is tree-structured, then one can instead use a faster bottom-up approach. We also extend these methods to other problems related to the cost-damage tradeoff, such as the costdamage Pareto front.

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Section: Relation To Knapsack Problems and Np-completenessmentioning

confidence: 99%