@article{22291,
  abstract     = {Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and fast-to-compute invariant known as the persistence diagram. However, this is no longer the case for maps between persistence modules (i.e. persistence maps). We propose a new invariant for persistence maps, consisting of a partial matching between the persistence diagrams of the domain and codomain modules. We show that this invariant is additive with respect to the direct sum decomposition of persistence maps, is more discriminative than the image module, and is computable in cubic time. Furthermore, we provide an implementation and demonstrate its efficiency by integrating it with edge collapse techniques for flag complexes (e.g., Vietoris–Rips complexes). As a key technical contribution, we describe how to induce a persistence map between two flag complexes that have been independently simplified via edge collapses, even when a direct simplicial map between them is no longer available.},
  author       = {Gonzalez-Diaz, Rocio and Soriano Trigueros, Manuel and Torras-Casas, Alvaro},
  issn         = {1095-855X},
  journal      = {Journal of Symbolic Computation},
  keywords     = {Persistence module, Persistence map, Persistent homology},
  publisher    = {Elsevier},
  title        = {{Additive partial matchings induced by persistence maps}},
  doi          = {10.1016/j.jsc.2026.102598},
  volume       = {138},
  year         = {2026},
}

@article{4060,
  abstract     = {This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are co-planar, It also presents an algorithm that in O(n log n) time constructs a tetrahedrization of a set of n points consisting of at most 3n-11 tetrahedra.},
  author       = {Edelsbrunner, Herbert and Preparata, Franco and West, Douglas},
  issn         = {1095-855X},
  journal      = {Journal of Symbolic Computation},
  number       = {3-4},
  pages        = {335 -- 347},
  publisher    = {Elsevier},
  title        = {{Tetrahedrizing point sets in three dimensions}},
  doi          = {10.1016/S0747-7171(08)80068-5},
  volume       = {10},
  year         = {1990},
}

@article{4106,
  abstract     = {Let B be a set of nb black points and W a set of nw, white points in the Euclidean plane. A line h is said to bisect B (or W) if, at most, half of the points of B (or W) lie on any one side of h. A line that bisects both B and W is called a ham-sandwich cut of B and W. We give an algorithm that computes a ham-sandwich cut of B and W in 0((nh+nw) log (min {nb, nw}+ 1)) time. The algorithm is considerably simpler than the previous most efficient one which takes 0((nb + nw) log (nb + nw)) time.},
  author       = {Edelsbrunner, Herbert and Waupotitsch, Roman},
  issn         = {1095-855X},
  journal      = {Journal of Symbolic Computation},
  number       = {2},
  pages        = {171 -- 178},
  publisher    = {Elsevier},
  title        = {{Computing a ham-sandwich cut in two dimensions}},
  doi          = {10.1016/S0747-7171(86)80020-7},
  volume       = {2},
  year         = {1986},
}

@article{4120,
  abstract     = {Let P be a set of n points in the Euclidean plane and let C be a convex figure. We study the problem of preprocessing P so that for any query point q, the points of P in C+q can be retrieved efficiently. If constant time sumces for deciding the inclusion of a point in C, we then demonstrate the existence of an optimal solution: the algorithm requires O(n) space and O(k + log n) time for a query with output size k. If C is a disk, the problem becomes the wellknown fixed-radius neighbour problem, to which we thus provide the first known optimal solution.},
  author       = {Chazelle, Bernard and Edelsbrunner, Herbert},
  issn         = {1095-855X},
  journal      = {Journal of Symbolic Computation},
  number       = {1},
  pages        = {47 -- 56},
  publisher    = {Elsevier},
  title        = {{Optimal solutions for a class of point retrieval problems}},
  doi          = {10.1016/S0747-7171(85)80028-6},
  volume       = {1},
  year         = {1985},
}