We give an algorithm for bichromatic line segment intersection counting that runs in O(n √ log n) time under the word RAM model via a reduction to dynamic predecessor search, offline point location, and offline dynamic ranking. This algorithm is the first to solve bichromatic line segment intersection counting in o(n log n) time.

Suppose M1 and M2 are two special Lagrangian submanifolds with boundary of R , n ≥ 3, that intersect transversally at one point p. The set M1 ∪M2 is a singular special Lagrangian variety with an isolated singularity at the point of intersection. Suppose further that the tangent planes at the intersection satisfy an angle criterion (which always holds in dimension n = 3). Then, M1 ∪ M2 is regula...

This paper is concerned with the problem of finding a representative sample of Pareto-optimal points inmulti-objective optimization. The Normal Boundary Intersection algorithm is a scalarization scheme for generating a set of evenly spaced Efficient solutions. A drawback of this algorithm is that Pareto-optimality of solutions is not guaranteed. The contributions of this paper are two-fold. Fir...

The creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {xi}~= 1, of jump discontinuities. Let S be the smallest closed set which satisfies: (i) S is a union of forward characteristics. (ii) S contains all the forward characteristics from the points {xi}~= 1" (iii) if two fo...

The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a, b, c, d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindström-GesselViennot theorem leads to a formula as a sum of...

Using a new technique, we prove a rich family of special cases of the matroid intersection conjecture. Roughly, we prove the conjecture for pairs of tame matroids which have a common decomposition by 2-separations into finite parts.

We present an optimal cache-oblivious algorithm for finding all intersections between a set of non-intersecting red segments and a set of non-intersecting blue segments in the plane. Our algorithm uses O( B logM/B N B + T/B) memory transfers, where N is the total number of segments, M and B are the memory and block transfer sizes of any two consecutive levels of any multilevel memory hierarchy,...

The intersection of line segments has already been studied by several authors. Several problems occurs when using floating point representation, in which number comparison is performed using a tolerance value. One of the main problems is the non-transitive property, as it may lead to incorrect results. Thus, fixed precision is preferred because it solves several problems. However, fixed precisi...

In this paper, we present an O(r n) algorithm for the linear matroid parity problem. Our solution technique is to introduce a modest generalization, the non-simple parity problem, and identify an important subclass of non-simple parity problems called 'easy' parity problems which can be solved as matroid intersection problems. We then show how to solve any linear matroid parity problem parametr...

The independent assignment problem (or the weighted matroid intersection problem) is extended using Dress-Wenzel’s matroid valuations, which are attached to the vertex set of the underlying bipartite graph as an additional weighting. Specifically, the problem considered is: Given a bipartite graph G = (V , V −;A) with arc weight w : A → R and matroid valuations ω and ω− on V + and V − respectiv...