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Ahmad Abdi's Publications

Preprints
  • On packing dijoins in digraphs and weighted digraphs (pdf, talk)
      Abdi, Cornuéjols, and Zlatin
      Submitted (2022)
      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
      To be submitted
      Extended abstract to appear in IPCO 2022
      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
      Submitted (2022)
      Keywords: Ideal clutter, filter oracle, property testing, cuboid, cube-ideal set, minor
  • A min-max theorem for clean tangled clutters (pdf)
      Abdi and Cornuéjols
      Submitted (2022)
      Keywords: clean tangled clutter, min-max theorem, notch, girth, covering number
  • On dyadic fractional packings of T-joins (pdf)
      Abdi, Cornuéjols and Palion
      Submitted (2021)
      Keywords: dyadic linear programming, Edmonds-Johnson theorem, Dyadic Conjecture, matching lattice, Petersen graph
Published papers
  • 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
  • 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
  • Idealness of k-wise intersecting families (extended abstract, pdf and erratum, talk, another talk)
      Abdi, Cornuéjols, Huynh and Lee
      Math Programming 192:29–50 (2022)
      Erratum appeared in Math 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
  • 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
      Math 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 Apr 20, 2022.