Ahmad Abdi's Publications

Preprints

• 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
• The rainbow covering number of clean tangled clutters (pdf)
  Abdi and Cornuéjols
  Manuscript (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 (2025), to appear
  Keywords: strongly connected orientation, crossing family, submodular flow, generalized set covering, total dual integrality, min-max theorem
• Strongly connected orientations and integer lattices (extended abstract, pdf)
  Abdi, Cornuéjols, Liu, and Silina
  Submitted (2025)
  Extended abstract to appear in IPCO 2025
  Keywords: strongly connected orientation, M-convex set, Hilbert basis, integer lattice, integral basis, Woodall’s conjecture

Published papers

• From coordinate subspaces over finite fields to ideal multipartite uniform clutters (pdf)
  Abdi and Lee
  Mathematical Programming (2024) https://doi.org/10.1007/s10107-024-02155-3
  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 (2024) https://doi.org/10.1007/s10107-024-02146-4
  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
  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
• 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
  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 May 20, 2025.