[{"key":"dc.contributor.author","value":"Swamy, Chaitanya","language":null},{"key":"dc.date.accessioned","value":"2018-05-13T05:02:07Z","language":null},{"key":"dc.date.available","value":"2018-05-13T05:02:07Z","language":"*"},{"key":"dc.date.issued","value":"2017-11-13T10:30","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-201711131030-Swamy","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-17w5133-25299","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/65829","language":null},{"key":"dc.description.abstract","value":"Interdiction problems investigate the sensitivity of an underlying optimization problem with respect to removal of a limited set of underlying elements in order to identify vulnerable spots for possible reinforcement or disruption. We consider the MST-interdiction problem: given a multigraph G with weights and interdiction costs on the edges, and an interdiction budget B, find a set R of edges of total interdiction cost at most B so as to maximize the weight of an MST of G-R.\n\nOur main result is a 4-approximation algorithm for this problem. This improves upon the previous-best 14-approximation due to Zenklusen, and notably, our analysis is also significantly simpler and cleaner. Whereas Zenklusen uses a greedy algorithm with an involved analysis to extract a good interdiction set from an over-budget set, we utilize a generalization of knapsack called the tree knapsack problem that nicely captures the key combinatorial aspects of this \"extraction problem.\" We prove a simple, yet strong, LP-relative approximation bound for tree knapsack, which leads to our improved guarantees for MST interdiction. Our algorithm and analysis are nearly tight, as we show that one cannot achieve an approximation ratio better than 3 relative to the upper bound used in our (and the prior) analysis. Our guarantee for MST-interdiction yields an 8-approximation for metric-TSP interdiction. We also show that the maximum-spanning-tree interdiction problem is at least as hard to approximate as the minimization version of densest-k-subgraph.\n\nThis is joint work with Andre Linhares.","language":null},{"key":"dc.format.extent","value":"32 minutes","language":null},{"key":"dc.format.mimetype","value":"video\/mp4","language":null},{"key":"dc.language.iso","value":"eng","language":null},{"key":"dc.publisher","value":"Banff International Research Station for Mathematical Innovation and Discovery","language":null},{"key":"dc.relation","value":"17w5133: Approximation Algorithms and the Hardness of Approximation","language":null},{"key":"dc.relation.ispartofseries","value":"BIRS Workshop Lecture Videos (Banff, Alta)","language":null},{"key":"dc.rights","value":"Attribution-NonCommercial-NoDerivatives 4.0 International","language":null},{"key":"dc.rights.uri","value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","language":null},{"key":"dc.subject","value":"Mathematics","language":null},{"key":"dc.subject","value":"Computer science","language":null},{"key":"dc.subject","value":"Operations research, mathematical programming","language":null},{"key":"dc.subject","value":"Theoretical computer science","language":null},{"key":"dc.title","value":"Improved Algorithms for MST and Metric-TSP Interdiction","language":null},{"key":"dc.type","value":"Moving Image","language":null},{"key":"dc.description.affiliation","value":"Non UBC","language":null},{"key":"dc.description.reviewstatus","value":"Unreviewed","language":null},{"key":"dc.description.notes","value":"Author affiliation: University of Waterloo","language":null},{"key":"dc.description.scholarlevel","value":"Faculty","language":null},{"key":"dc.date.updated","value":"2018-05-13T05:02:07Z","language":null}]