Associate professor, math & computer science
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- Dunn 226
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My research program considers dynamic processes occurring on networks with main objectives to determine optimal resource allocation and long term behaviour of dynamic processes.
Graph Searching and Dynamic Domination Problems
Graph searching and dynamic domination problems focus on the following question: how can the activity of an adversary be neutralized in a network? A collection of agents move around a network according to a rule set. In graph searching, the goal is generally to locate a hidden mobile adversary, while for dynamic domination problems, the goal is generally to defend against a sequence of adversarial attacks. The study of such network security problems has largely been inspired by foundational issues in discrete mathematics and theoretical computer science.
With respect to adversarial attacks in networks, such attacks can occur in a variety of ways: spreading a virus through a network, damaging targeted or random nodes, or by a simple intrusion on a network. In such network security problems, agents occupy a set of nodes on the network and move, according to a set of rules, in response to attacks. In most models, determining the minimum number of resources (i.e. agents) required to successfully combat a sequence of adversarial attacks is difficult, but many useful algorithmic and theoretical results have been obtained. The fundamental question in such models is: how can adversarial actions in a network be economically combatted?
Long Term Behaviours on Closed Networks
In Chip Firing and Graph Diffusion problems, a finite number of chips are initially places on nodes of a graph and at each step, chips are moved from node to node according to a ruleset. Given an evolutionary rule by which assets are moved within a network, a fundamental question is: what is the long term behaviour of the network?
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