Allocating Limited Resources to Protect a Massive Number of Targets Using a Game Theoretic Model

Liu, Xu; Di, Xiaoqiang; Li, Jinqing; Wang, Huan; Zhao, Jianping; Yang, Huamin; Lin, Cong; Jiang, Yuming

doi:10.1155/2019/5475341

Cited by 5 publications

(2 citation statements)

References 34 publications

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“…Our complete bipartite graph has O(n 2 ) vertices (by construction), so our algorithm takes O(n 6 ) time. Observe that when t ≪ s, we have s * t ≈ n � O(n) (for example, when a very large number of distributed access points must be matched to a much smaller number of mobile stations [21], or limited resources are matched to a massive number of targets [22]), and thus, our algorithm runs in O(n 3 ) time. Moreover, in bipartite graphs with low-range edge weights, our algorithm runs well due to [19] As an example, consider two sets…”

Section: Tus W(main(m)) � C(l)mentioning

confidence: 99%

Computing a Many-to-Many Matching with Demands and Capacities between Two Sets Using the Hungarian Algorithm

Rajabi-Alni

Bagheri

2023

Journal of Mathematics

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A many-to-many matching (MM) between two sets matches each element of one set to at least one element of the other set. A general case of the MM is the many-to-many matching with demands and capacities (MMDC) satisfying given lower and upper bounds on the number of elements matched to each element. In this article, we give a polynomial-time algorithm for finding a minimum-cost MMDC between two sets using the well-known Hungarian algorithm.

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Section: Tus W(main(m)) � C(l)mentioning

confidence: 99%

Computing a Many-to-Many Matching with Demands and Capacities between Two Sets Using the Hungarian Algorithm

Rajabi-Alni

Bagheri

2023

Journal of Mathematics

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“…To solve the above issue, we propose an active defense model. Liu et al 3 pointed out that defenders can attempt to stop attacks by making them pay a large enough cost to attackers. In this article, we adopt their view.…”

Section: Introductionmentioning

confidence: 99%

An active defense model based on situational awareness and firewalls

Xiao

et al. 2023

Concurrency and Computation

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With the rapid development of the internet, cyberspace security issues have become increasingly prominent. The importance of constructing a cyberspace security system is self-evident, but compared with attackers, defenders in cyberspace are in a castle-like passive defense state in most cases. Therefore, building a reliable, accurate, timely, and active defense system is challenging. The key is to accurately focus on defense priorities, the anticipation of attackers who will likely succeed, and blocking attacks in a timely manner. In this article, we propose an active defense model based on the interaction of situational awareness and firewalls. First, by biasing the integrity, confidentiality, and availability of assets to get the score of assets, and using the Common Vulnerability Scoring System to assess the threat level of assets, we combine the two to determine the maximum system damage that the asset will suffer if it is lost, and then focus on defense. Meanwhile, log analysis of the network situational awareness platform can predict successful attackers, and then the linked firewall strategy can block these attacks in time before the attackers obtain attack gains. After that, we force the attackers to give up their attacks on the target by increasing the attack cost.We compared our model with iptables auto-blocking and nginx auto-blocking, and our model excelled them across the board in terms of comprehensiveness and false positive rate. The experimental results verify thar our active defense model proposed in this article can better reduce the defense cost and increase the attack cost, thus achieving the relatively defense goal. K E Y W O R D Sactive defense, cyber attack and defense, defense cost, game theory INTRODUCTIONWith the development of information technology, cyberspace has become the fifth space after "land, sea, air, and sky", and the security of cyberspace is directly related to the sovereign security of the country. Cyber attack and defense have become hot spots in current cybersecurity research. The objectives of cyber attackers include collecting information about a target, paralyzing the target service, entering the target and stealing data, while the objectives of cyber defenders are to keep the service running normally and stop attackers. Scanning of the target system is something that a cyber attacker must do before launching cyber attacks, which helps the attacker gain access to exploitable vulnerabilities in the target system to compromise the network. The purpose of such a scan is to understand the configurations of target systems, including but not limited to the target system's operating system, IP address, running services, software versions, existing common vulnerabilities & exposures(CVEs), weak passwords, and so on. How to prevent attackers from obtaining the scan results or prevent the attacker from using the scan results for other benefits is the goal

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Allocation of limited resources under quadratic constraints

2022

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The proper allocation/distribution of limited resources is a traditional problem with various applications. The mathematical formulation of such problems usually includes constraints describing the set of feasible solutions (feasible set), from which the (nearly) optimal or equilibrium solution should be selected. Often the feasible set is more difficult to determine than to find the optimal or equilibrium solution. Alternatively, the already known feasible set often makes it easier to select the optimal or equilibrium solution. In some other cases, any feasible solutions are the same satisfactory, additional optimization is needless. Accordingly, the main or only task in many cases is to determine the feasible set itself. In the paper, a new theorem is proved for the explicit expression of properly assigned (dependent) variables by means of the other (independent) variables in a system of inequality and quadratic equality constraints. The sum of the (nonnegative) variables can be either prefixed or not. The constraints may describe the feasible set in various resource allocation tasks (possibly in optimization or game-theoretical contexts) or in other problems. Two new lemmas are proved for supporting the proof of the above mentioned theorem, nevertheless, they can also be considered independent results, which may help future mathematical derivations. Supported by a further new lemma, a practical algorithm is derived for assigning in a feasible way the independent variables, to which (possibly limited) arbitrary nonnegative values can be prescribed. Various practical examples are provided to facilitate utilizing the results.

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Allocating Limited Resources to Protect a Massive Number of Targets Using a Game Theoretic Model

Cited by 5 publications

References 34 publications

Computing a Many-to-Many Matching with Demands and Capacities between Two Sets Using the Hungarian Algorithm

Computing a Many-to-Many Matching with Demands and Capacities between Two Sets Using the Hungarian Algorithm

An active defense model based on situational awareness and firewalls

Allocation of limited resources under quadratic constraints

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