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Ahmad Abdi's Publications

  • Testing the max-flow min-cut property and the replication conjecture (pdf)
      Abdi and Schwarcz
      Submitted (2026)
      Keywords: set covering, total dual integrality, max-flow min-cut property, replication conjecture, square-free monomial ideal, formal verification
  • Cosigning crossing families and outer-planar gadgets (extended abstract, pdf)
      Abdi, Dalirrooyfard, and Neuwohner
      To be submitted (2026)
      Extended abstract to appear in ISCO 2026
      Keywords: graph orientation, crossing family, submodular function minimization, disjoint dijoins, planar graph, polynomial algorithm
  • Lower bounds for cube-ideal set-systems (pdf)
      Abdi, Cornuéjols, Dadush, and Dalirrooyfard
      Submitted (2025)
      Keywords: cube-ideal set-system, VC dimension, centrally symmetric hypercube, mixed graph, strong orientation, perfect matching
  • Integral bases, perfect matchings, and the Petersen graph (pdf, slides)
      Abdi and Silina
      Mathematical Programming, to appear (2026)
      Keywords: matching-covered graph, matching lattice, lattice basis, Petersen graph, Birkhoff–von Neumann graph, separating cut
  • Strongly connected orientations and integer lattices (extended abstract, pdf, talk)
      Abdi, Cornuéjols, Liu, and Silina
      Mathematics of Operations Research, to appear (2026)
      Extended abstract appeared in IPCO 2025, LNCS 15620, pp. 1-14
      Keywords: strongly connected orientation, M-convex set, Hilbert basis, integer lattice, integral basis, Woodall’s conjecture
  • The rainbow covering number of clean tangled clutters (pdf)
      Abdi and Cornuéjols
      arXiv:2509.08505 (2025)
      Keywords: clutter, blocker, rainbow covering number, clean clutter
  • Strong orientation of a connected graph for a crossing family (pdf)
      Abdi, Dalirrooyfard, and Neuwohner
      Operations Research Letters 62:107333 (2025)
      Keywords: strongly connected orientation, crossing family, submodular flow, generalized set covering, total dual integrality, min-max theorem
  • From coordinate subspaces over finite fields to ideal multipartite uniform clutters (pdf)
      Abdi and Lee
      Mathematical Programming 213:823–861 (2025)
      Keywords: vector space over finite field, multipartite uniform clutter, ideal clutter, the max-flow min-cut property, minor-closed property, matroid
  • Dyadic linear programming and extensions (pdf)
      Abdi, Cornuéjols, Guenin and Tunçel
      Mathematical Programming 213:473–516 (2025)
      Keywords: Linear programming, integer programming, dyadic rational, floating-point arithmetic, polynomial algorithm, dense abelian subgroup
  • Arc connectivity and submodular flows in digraphs (pdf, talk, slides)
      Abdi, Cornuéjols, and Zambelli
      Combinatorica 44:1069–1090 (2024)
      Keywords: graph orientation, k-arc-connected flip, weak orientation theorem, Woodall’s conjecture, submodular flows, total dual integrality
  • On packing dijoins in digraphs and weighted digraphs (pdf, talk)
      Abdi, Cornuéjols, and Zlatin
      SIAM Journal on Discrete Mathematics 37(4):2417-2461 (2023)
      Keywords: min-max theorem, dijoins, strongly base orderable matroid, packing common bases, submodular function, integer decomposition property
  • Total dual dyadicness and dyadic generating sets (extended abstract, pdf)
      Abdi, Cornuéjols, Guenin and Tunçel
      Mathematical Programming 206:125-143 (2024)
      Extended abstract appeared in IPCO 2022, LNCS 13265, pp. 1-14
      Keywords: dyadic linear programming, property testing, Smith normal form, Hilbert basis, circuits, perfect matchings
  • Testing idealness in the filter oracle model (pdf)
      Abdi, Cornuéjols, Guenin and Tunçel
      Operation Research Letters 50(6):753--755 (2022)
      Keywords: Ideal clutter, filter oracle, property testing, cuboid, cube-ideal set, minor
  • On dyadic fractional packings of T-joins (pdf)
      Abdi, Cornuéjols and Palion
      SIAM Journal on Discrete Mathematics 36(3):2445-2451 (2022)
      Keywords: dyadic linear programming, Edmonds-Johnson theorem, Dyadic Conjecture, matching lattice, Petersen graph
  • Clean clutters and dyadic fractional packings (pdf, talk)
      Abdi, Cornuéjols, Guenin and Tunçel
      SIAM Journal on Discrete Mathematics 36(2):1012-1037 (2022)
      Keywords: dyadic linear programming, clean tangled clutter, Dyadic Conjecture, filter oracle, quasi-polynomial time algorithm
  • Clean tangled clutters, simplices, and projective geometries (pdf)
      Abdi, Cornuéjols and Superdock
      Journal of Combinatorial Theory, Series B 154:60-92 (2022)
      Keywords: clean tangled clutter, simplex, projective geometry over GF(2), cuboid, Fano minor
  • Idealness of k-wise intersecting families (extended abstract, pdf and erratum, talk, another talk)
      Abdi, Cornuéjols, Huynh and Lee
      Mathematical Programming 192:29–50 (2022)
      Erratum appeared in Mathematical Programming 192:51–55 (2022)
      Extended abstract appeared in IPCO 2020, LNCS 12125, pp. 1–12
      Keywords: ideal clutter, k-wise intersecting clutter, chromatic number, binary clutter, 8-flow theorem, cuboid
  • A new infinite family of ideal minimally non-packing clutters (pdf)
      Abdi, Cornuéjols and Superdock
      Discrete Mathematics 344(7):112413 (2021)
      Keywords: the τ=2 Conjecture, packing property, cuboid, dijoins
  • The max-flow min-cut property and ±1-resistant sets (pdf)
      Abdi and Cornuéjols
      Discrete Applied Mathematics 289:455-476 (2020)
      Keywords: cuboid, cube-ideal set, resistant set, structure theorem, excluded minor characterization
  • Resistant sets in the unit hypercube (pdf)
      Abdi, Cornuéjols and Lee
      Mathematics of Operations Research 46(1):82-114 (2020)
      Keywords: cuboid, cube-ideal set, resistant set, polynomial time algorithm, Replication Conjecture, packing property
  • Intersecting restrictions in clutters (pdf)
      Abdi, Cornuéjols and Lee
      Combinatorica 40:605–623 (2020)
      Keywords: property testing, polynomial time algorithm, the τ=2 Conjecture, intersecting clutter, clean clutter
  • Cuboids, a class of clutters (pdf, code)
      Abdi, Cornuéjols, Guričanová and Lee
      Journal of Combinatorial Theory, Series B 142:144-209 (2020)
      Keywords: cuboid, the τ=2 Conjecture, the Flowing Conjecture, the Replication Conjecture, cube-ideal set, strict polarity
  • Idealness and 2-resistant sets (pdf)
      Abdi and Cornuéjols
      Operation Research Letters 47(5):358-362 (2019)
      Keywords: cube-ideal set, resistant set, structure theorem, excluded minor characterization
  • Identically self-blocking clutters (pdf)
      Abdi, Cornuéjols and Lee
      IPCO 2019, LNCS 11480, pp. 1–12
      Keywords: ideal clutter, identically self-blocking clutter, gauge duality, quadratic programming, packing number, cuboid
  • The two-point Fano and ideal binary clutters (extended abstract, pdf)
      Abdi and Guenin
      Combinatorica 39(4): 753-777 (2019)
      Extended abstract appeared in IPCO 2017, LNCS 10328, pp. 1–12
      Keywords: the Flowing Conjecture, ideal clutter, blocker, Lehman's theorem, signed binary matroid, Fano minor
  • The minimally non-ideal binary clutters with a triangle (pdf, talk)
      Abdi and Guenin
      Combinatorica 39(4): 719-752 (2019)
      Keywords: the Flowing Conjecture, Lehman's theorem, blocker, signed binary matroid, Fano minor, odd-K5 minor
  • Deltas, extended odd holes and their blockers (pdf)
      Abdi and Lee
      Journal of Combinatorial Theory, Series B 136:193-203 (2019)
      Keywords: Minor, delta, extended odd hole, blocker, filter oracle
  • Delta minors, delta free clutters, and entanglement (pdf)
      Abdi and Pashkovich
      SIAM Journal on Discrete Mathematics 32(3):1750-1774 (2018)
      Keywords: convex union,, delta, lift, projection, opposite pair in clutter, blocker
  • Ideal clutters that do not pack (pdf)
      Abdi, Cornuéjols and Pashkovich
      Mathematics of Operations Research 43(2):533-553 (2018)
      Keywords: Ideal clutter, the packing property, the τ=2 Conjecture, cuboid, coexclusive pair in clutter, delta
  • Opposite elements in clutters (pdf)
      Abdi, Fukasawa and Sanità
      Mathematics of Operations Research 43(2):428-459 (2018)
      Keywords: Ideal clutter, the packing property, delta, opposite pair in clutter, bidirecting, Steiner tree
  • Packing odd T-joins with at most two terminals (extended abstract, pdf, talk)
      Abdi and Guenin
      Journal of Graph Theory 87:587-652 (2018)
      Extended abstract appeared in IPCO 2014, LNCS 8494, pp. 1-12
      Keywords: the Cycling Conjecture, odd T-join, graphs on surfaces, excluded minor characterization, Fano minor, odd-K5 minor
  • Lehman's theorem and the directed Steiner tree problem (pdf)
      Abdi, Feldmann, Guenin, Könemann and Sanità
      SIAM Journal on Discrete Mathematics 30(1):141-153 (2016)
      Keywords: Ideal clutter, Steiner tree, Lehman's theorem, series-parallel graph, arborescence
  • On the mixing set with a knapsack constraint (pdf)
      Abdi and Fukasawa
      Mathematical Programming Series B 157(1):191-217 (2016)
      Keywords: chance-constrained programming, mixing set, knapsack contraint, facet-defining inequality, extended formulation
Last update was on July 10, 2026.