6,491 research outputs found
Surface cubications mod flips
Let be a compact surface. We prove that the set of surface
cubications modulo flips, up to isotopy, is in one-to-one correspondence with
.Comment: revised version, 18
Simplex and Polygon Equations
It is shown that higher Bruhat orders admit a decomposition into a higher
Tamari order, the corresponding dual Tamari order, and a "mixed order." We
describe simplex equations (including the Yang-Baxter equation) as realizations
of higher Bruhat orders. Correspondingly, a family of "polygon equations"
realizes higher Tamari orders. They generalize the well-known pentagon
equation. The structure of simplex and polygon equations is visualized in terms
of deformations of maximal chains in posets forming 1-skeletons of polyhedra.
The decomposition of higher Bruhat orders induces a reduction of the
-simplex equation to the -gon equation, its dual, and a compatibility
equation
Bi-Criteria and Approximation Algorithms for Restricted Matchings
In this work we study approximation algorithms for the \textit{Bounded Color
Matching} problem (a.k.a. Restricted Matching problem) which is defined as
follows: given a graph in which each edge has a color and a profit
, we want to compute a maximum (cardinality or profit)
matching in which no more than edges of color are
present. This kind of problems, beside the theoretical interest on its own
right, emerges in multi-fiber optical networking systems, where we interpret
each unique wavelength that can travel through the fiber as a color class and
we would like to establish communication between pairs of systems. We study
approximation and bi-criteria algorithms for this problem which are based on
linear programming techniques and, in particular, on polyhedral
characterizations of the natural linear formulation of the problem. In our
setting, we allow violations of the bounds and we model our problem as a
bi-criteria problem: we have two objectives to optimize namely (a) to maximize
the profit (maximum matching) while (b) minimizing the violation of the color
bounds. We prove how we can "beat" the integrality gap of the natural linear
programming formulation of the problem by allowing only a slight violation of
the color bounds. In particular, our main result is \textit{constant}
approximation bounds for both criteria of the corresponding bi-criteria
optimization problem
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