Missile Defense Is NP-Complete

6 hours ago

Missile defense is an NP-complete problem due to the complexity of resource allocation.
Single Shot Probability of Kill (SSPK) measures the effectiveness of an interceptor, with the U.S. GMD system having an SSPK of 56%.
Multiple interceptors can be assigned to a single warhead to increase the probability of successful interception, but this is based on optimistic independence assumptions.
The real-world effectiveness is lower due to factors like detection, tracking, and classification failures, formalized by Wilkening's probability model.
The Weapon-Target Assignment (WTA) problem is NP-complete, involving complex decision-making on interceptor allocation against multiple warheads and decoys.
Recent advancements allow solving large-scale WTA problems quickly, but attackers can still overwhelm defenses by increasing the number of warheads and decoys.
Current U.S. missile defense inventory is limited, with 44 GBIs providing defense against a small number of ICBMs, highlighting thin margins.
Directed energy is proposed as an alternative but comes with its own challenges.
Missile defense is a two-sided problem, with attackers having structural advantages like choosing the problem size and observing defenses beforehand.

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