The Maximum Weight Connected Subgraph Problem on Subclasses of Graphs
Location
Oyate Hall
Event Website
https://2026undergraduateresearchsy.sched.com/event/2Ix98/the-maximum-weight-connected-subgraph-problem-on-subclasses-of-graphs
Start Date
15-4-2026 6:00 PM
End Date
15-4-2026 8:00 PM
Description
Consider a telecommunications network where a company wants to strategically select locations for cellular towers which also ensure a tower-to-tower connection exists between active sites. Each location has the potential to generate income for the company based on the population the tower would serve. Any connection between two towers will result in some infrastructure cost, so the provider must balance the value of coverage with the expense of a link. This problem is an example of an application of the Maximum Weight Connected Subgraph Problem, Net Worth version (MWCSP-NW). Mathematically, the problem is defined as follows: given a connected graph G = (V, E), a positive real-valued prize function on the vertices, V, and a positive real-valued weight function on the edges, E, we would like to find a connected subgraph which maximizes total vertex prizes minus total edge weights. In our application, the tower-to-tower connections can be thought of as the edges and the cost of establishing these connections as the edge weight function, while the potential tower sites are represented by vertices with prizes determined based on the population served. It has been shown that for a general graph, MWCSP-NW is NP-Hard, meaning there exists no known efficient algorithm to solve it, and there probably never will be. Therefore, it would be beneficial to find subclasses of graphs where we can provably solve the MWCSP-NW. We will show that MWCSP-NW can be solved efficiently to optimality on these subclasses of graphs.
Publication Date
2026
The Maximum Weight Connected Subgraph Problem on Subclasses of Graphs
Oyate Hall
Consider a telecommunications network where a company wants to strategically select locations for cellular towers which also ensure a tower-to-tower connection exists between active sites. Each location has the potential to generate income for the company based on the population the tower would serve. Any connection between two towers will result in some infrastructure cost, so the provider must balance the value of coverage with the expense of a link. This problem is an example of an application of the Maximum Weight Connected Subgraph Problem, Net Worth version (MWCSP-NW). Mathematically, the problem is defined as follows: given a connected graph G = (V, E), a positive real-valued prize function on the vertices, V, and a positive real-valued weight function on the edges, E, we would like to find a connected subgraph which maximizes total vertex prizes minus total edge weights. In our application, the tower-to-tower connections can be thought of as the edges and the cost of establishing these connections as the edge weight function, while the potential tower sites are represented by vertices with prizes determined based on the population served. It has been shown that for a general graph, MWCSP-NW is NP-Hard, meaning there exists no known efficient algorithm to solve it, and there probably never will be. Therefore, it would be beneficial to find subclasses of graphs where we can provably solve the MWCSP-NW. We will show that MWCSP-NW can be solved efficiently to optimality on these subclasses of graphs.
https://digitalcommons.morris.umn.edu/urs_event/2026/posters/2