Marcos Kiwi

Publications (8)1.03 Total impact

• Source

  Available from: ArXiv

  Article: Computational Hardness of Enumerating Satisfying Spin-Assignments in Triangulations

  Andrea Jiménez, Marcos Kiwi
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  ABSTRACT: Satisfying spin-assignments in triangulations of a surface are states of minimum energy of the antiferromagnetic Ising model on triangulations which correspond (via geometric duality) to perfect matchings in cubic bridgeless graphs. In this work we show that it is NP-complete to decide whether or not a surface triangulation admits a satisfying spin-assignment, and that it is #P-complete to determine the number of such assignments. Both results are derived via an elaborate (and atypical) reduction that maps a Boolean formula in 3-conjunctive normal form into a triangulation of an orientable closed surface.
  07/2011;
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  Available from: ArXiv

  Article: Counting perfect matchings of cubic graphs in the geometric dual

  Andrea Jiménez, Marcos Kiwi
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  ABSTRACT: Lov\'asz and Plummer conjectured, in the mid 1970's, that every cubic graph G with no cutedge has an exponential in |V(G)| number of perfect matchings. In this work we show that every cubic planar graph G whose geometric dual graph is a stack triangulation has at least 3 times the golden ratio to |V(G)|/72 distinct perfect matchings. Our work builds on a novel approach relating Lov\'asz and Plummer's conjecture and the number of so called groundstates of the widely studied Ising model from statistical physics. Comment: 18 pages, 8 figures
  10/2010;
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  Available from: ArXiv

  Article: Satisfying states of triangulations of a convex n-gon

  Andrea Jiménez, Marcos Kiwi, Martin Loebl
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  ABSTRACT: In this work we count the number of satisfying states of triangulations of a convex n-gon using the transfer matrix method. We show an exponential (in n) lower bound. We also give the exact formula for the number of satisfying states of a strip of triangles. Comment: 17 pages, 6 figures
  12/2009;
• Source

  Available from: uchile.cl

  Article: Towards the Distribution of the Size of a Largest Planar Matching and Largest Planar Subgraph in Random Bipartite Graphs

  Marcos Kiwi, Martin Loebl
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  ABSTRACT: We address the following question: When a randomly chosen regular bipartite multi--graph is drawn in the plane in the ``standard way'', what is the distribution of its maximum size planar matching (set of non--crossing disjoint edges) and maximum size planar subgraph (set of non--crossing edges which may share endpoints)? The problem is a generalization of the Longest Increasing Sequence (LIS) problem (also called Ulam's problem). We present combinatorial identities which relate the number of r-regular bipartite multi--graphs with maximum planar matching (maximum planar subgraph) of at most d edges to a signed sum of restricted lattice walks in Z^d, and to the number of pairs of standard Young tableaux of the same shape and with a ``descend--type'' property. Our results are obtained via generalizations of two combinatorial proofs through which Gessel's identity can be obtained (an identity that is crucial in the derivation of a bivariate generating function associated to the distribution of LISs, and key to the analytic attack on Ulam's problem). We also initiate the study of pattern avoidance in bipartite multigraphs and derive a generalized Gessel identity for the number of bipartite 2-regular multigraphs avoiding a specific (monotone) pattern.
  07/2007;
• Article: Expected Length of the Longest Common Subsequence for Large

  Marcos Kiwi, Depto Ing Matematica, Martin Loebl
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  ABSTRACT: r and upper bounds on k as well as a stronger version, due to Arratia and Steele, of the above stated conjecture.) An extended abstract of this work appears in Proc. 6th Latin American Theoretical Informatics Symposium (LATIN 2004), LNCS series, Springer, Berlin. A full version is available at the web page of the third author. Gratefully acknowledges the support of ICM P01-05 and Fondecyt 1010689. Gratefully acknowledges the support of ICM-P01-05. This work was done while visiting the Dept. Ing. Matematica, U. Chile. This research was done while visiting the Ctr. de Modelamiento Matematico, UMR{UChile 2071, U. Chile, Santiago, supported by Fondap in Applied Mathematics 2000-05. 1 The constant 2 in (1) arises from a connection with another celebrated problem, the distribution of LISN , the length of the longest increasing subsequence in a (uniform) random permutation of f1; 2; : : : ; Ng. Hammersley [4] proved the existence of = lim N!1 (E [LIS N ] = N) and conjec
  02/2004;
• Source

  Available from: ArXiv

  Article: Expected length of the longest common subsequence for large alphabets

  Marcos Kiwi, Martin Loebl, Jiří Matoušek
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  ABSTRACT: We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that E[L]/n converges to a constant γk. We prove a conjecture of Sankoff and Mainville from the early 1980s claiming that as k→∞.
  Advances in Mathematics. 09/2003;
• Article: Expected Length of the Longest Common Subsequence for Large

  Depto Ing Matem'atica, Marcos Kiwi, Martin Loebl
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  ABSTRACT: We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that E [L] =n converges to a constant fl k . We prove a conjecture of Sankoff and Mainville from the early 80's claiming that fl k k ! 2 as k !1.
  09/2003;
• Article: Largest planar matching in random bipartite graphs

  Marcos Kiwi, Martin Loebl
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  ABSTRACT: For a distribution over labeled bipartite (multi) graphs G = (W, M, E), |W| = |M| = n, let L(n) denote the size of the largest planar matching of G (here W and M are posets drawn on the plane as two ordered rows of nodes and edges are drawn as straight lines). We study the asymptotic (in n) behavior of L(n) for different distributions . Two interesting instances of this problem are Ulam's longest increasing subsequence problem and the longest common subsequence problem. We focus on the case where is the uniform distribution over the k-regular bipartite graphs on W and M. For k = o(n1/4), we establish that tends to 2 in probability when n → ∞. Convergence in mean is also studied. Furthermore, we show that if each of the n2 possible edges between W and M are chosen independently with probability 0 < p < 1, then L(n)/n tends to a constant p in probability and in mean when n → ∞. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 162–181, 2002
  Random Structures and Algorithms 08/2002; 21(2):162 - 181. · 1.03 Impact Factor