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UID:pretalx-juliacon-2026-3W9MAF@pretalx.com
DTSTART;TZID=CET:20260812T154500
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DESCRIPTION:The *cut norm* of a matrix measures the largest imbalance\, giv
 en by the maximum absolute sum of its entries over any choice of row and c
 olumn subsets. Computing this norm amounts to a combinatorial optimization
  problem that is *NP-hard*. It originates in graph theory and it plays a c
 entral role in the theory of graph limits\, where it defines a notion of d
 istance between large networks.\n\nWe first present an integer program\, m
 odeled in *JuMP.jl*\, and highlight the limitations in scalability. We the
 n introduce a heuristic based on repeatedly solving a bilinear relaxation 
 of the cut norm problem. Along the way\, we utilize *NLPModels.jl* to effi
 ciently represent the problem and solve the resulting nonlinear program us
 ing TRON from *JSOSolvers.jl*.  To explore the solution space effectively\
 , we employ a multi-start strategy initialized via a Sobol sequence genera
 ted with *Sobol.jl*.\n\nThrough benchmarks\, we show that the heuristic re
 covers optimal solutions on small instances and scales to significantly la
 rger matrices than the exact formulation. We also illustrate how the algor
 ithm can be used in the context of graph limit theory to measure the dista
 nce between large networks.
DTSTAMP:20260502T102651Z
LOCATION:Room 2
SUMMARY:Making the Cut Norm Practical: A Julia Ecosystem Approach - Martin 
 Köhler
URL:https://pretalx.com/juliacon-2026/talk/3W9MAF/
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