Models and Algorithms for Matching and Assignment Problems

A course by prof. Silvano Martello

  • Date:

    19 DECEMBER 2017
     from 14:30 to 19:30
  • Event location: School of Architecture and Engineering, viale del Risorgimento 2, Bologna - see agenda for rooms details

  • Type: Course

Course in common with other curricula.


  • Thursday November 30
    from 2.30 pm to 7.30 pm, room 5.6
  • Thursday December 7, 2017
    from 2:30 pm to 7:30 pm, room 5.6
  • Thursday December 14, 2017
    from 3:00 pm- 7:30 pm, room 5.1 
  • Tuesday December 19, 2017
    from 2:30 pm to 7:30 pm, room 5.2

Length: 20 hours


  1. Introduction: matching, assignment, graphs, bipartite graphs, adjacency matrix, incidence matrix;
  2. Theoretical foundations: matching problems, Hall’s marriage theorem, Koenig’s algorithm, augmenting path, complexity, stable marriage problem;
  3. Maximum matching applications: vehicle scheduling, time slot assignment (TDMA), open shop scheduling;
  4. Linear sum assignment problem: weighted matching, constraint matrix, unimodularity, duality, Egervary’s theorem, initialization algorithms;
  5. The Hungarian algorithm: main structure, rooted alternating tree, complexity, Kuhn’s algorithm, Jacobi’s theorem;
  6. Non-Hungarian algorithms: Dinic-Kronrod’s algorithm, primal simplex algorithms, Egervary’s algorithm, Birkhoff-Von Neumann theorem;
  7. Other linear assignment problems: k-cardinality assignment, bottleneck assignment, threshold algorithm, balanced assignment;
  8. Quadratic assignment problems: combinatorial formulation, complexity, integer quadratic formulation, inner product formulation, trace formulation, exact solution, heuristics.


Prof. Silvano Martello

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