Date of Award

12-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Operational Sciences

First Advisor

Richard F. Deckro, PhD

Abstract

Recognizing that Western societies and militaries depend on expansive networks, network complexities could conceal vulnerabilities and susceptibilities. Identifying nodes and edges an adversary could target is challenging, even in small networks. This research derives new mathematical formulations that solve the Isolation Set Problem (ISP) to help improve network operations analysis. The models developed in this dissertation to solve the ISP are the Effects Based Network Decay (E-BAND), the Reduced Effects Based Network Decay (R-BAND) models, and their respective dual formulations. Each formulation implemented various size reduction techniques on a current formulation, the Totally Unimodular Network Decay (TUND) model. Empirical testing compared solver run time for every model using randomly generated Erdos–Renyi and Barabasi–Albert graphs. Of the 29, 960 test runs executed across 3, 000 parameter instances, the E-BAND, R-BAND, and dual models identified optimal solutions more rapidly than the TUND model 99.9% of the time. The E-BAND and R-BAND models could conduct insightful network analysis but may leave decision-makers with the burden of coordinating many individual tasks.

AFIT Designator

AFIT-ENS-DS-23-D-007

Comments

An embargo was observed for posting this dissertation on AFIT Scholar.

Approved for public release, distribution unlimited. PA case number 88ABW/PA 2026-0587, 22 October 2026.

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