1. The Lenstra-Lenstra-Lovasz basis reduction algorithm (MS/PhD). Deng Chao.
    One of the most famous algorithms of the 20th century, which finds a short vector in a lattice. Applications range from cryptography through number theory and integer programming.
    From Grotschel-Lovasz-Schrijver: Geometric Algorithms, and Combinatorial Optimization, Springer (borrow book from instructor).
  2. Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems, (MS/PhD) Sudhanshu Singh. D. Applegate, Bill Cook, R. Bixby, and V. Chvatal
    How to solve those TSPs with 85 thousand cities? This paper explains how.
    Mathematical Programming (Series B) 97 (2003) 91--153.
  3. Sudoku: structure and strategy, by S. Provan (MS).
    Sudoku's integer programming formulation is intimately connected to IP theory. This paper describes how. Sean Skwerer.
    Available from the STOR webpage.
  4. An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming, by William Cook, Thomas Rutherford, Herbert E. Scarf, David Shallcross (PhD). Alex Mills.
    How to find that direction which produces a small number of branch-and-bound nodes? We can do it by solving a bunch of LPs.
    For hard integer programs, this effort is actually worth it! This paper describes why.
    ORSA Journal on Computing, 1993, volume 5, pages 206-212.
  5. Vasek Chvatal: Hard knapsack problems (PhD). Jianzhe Luo.
    A probabilistic model that explains, why most knapsack problems in a certain family are difficult.
    Operations Research, 1980, volume 28, pages 1402-1411.