Related papers: The fast intersection transform with applications …
We present an algorithm that computes the girth of the intersection graph of $n$ given line segments in the plane in $O(n^{1.483})$ expected time. This is the first such algorithm with $O(n^{3/2-\varepsilon})$ running time for a positive…
The edges of a graph are assigned weights and passage times which are assumed to be positive integers. We present a parallel algorithm for finding the shortest path whose total weight is smaller than a pre-determined value. In each step the…
Various applications of graphs, in particular applications related to finding shortest paths, naturally get inputs with real weights on the edges. However, for algorithmic or visualization reasons, inputs with integer weights would often be…
Set intersection is a fundamental operation in information retrieval and database systems. This paper introduces linear space data structures to represent sets such that their intersection can be computed in a worst-case efficient way. In…
We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
We consider the problem of augmenting an n-vertex graph embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present exact algorithms for the cases when (i) the input…
The goal of this paper is to design a simplex algorithm for linear programs on lattice polytopes that traces `short' simplex paths from any given vertex to an optimal one. We consider a lattice polytope $P$ contained in $[0,k]^n$ and…
We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in $\mathbb{R}^d$. In this setting, each vertex corresponds to a geometric object, and two…
We study a path-planning problem amid a set $\mathcal{O}$ of obstacles in $\mathbb{R}^2$, in which we wish to compute a short path between two points while also maintaining a high clearance from $\mathcal{O}$; the clearance of a point is…
We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…
Let $G$ be a unit disk graph in the plane defined by $n$ disks whose positions are known. For the case when $G$ is unweighted, we give a simple algorithm to compute a shortest path tree from a given source in $O(n\log n)$ time. For the case…
We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…
We solve two problems regarding the enumeration of lattice paths in $\mathbb{Z}^2$ with steps $(1,1)$ and $(1,-1)$ with respect to the major index, defined as the sum of the positions of the valleys, and to the number of certain crossings.…
Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…
Level-sensitive latches are widely used in high- performance designs. For such circuits efficient statistical timing analysis algorithms are needed to take increasing process vari- ations into account. But existing methods solving this…
We discuss the complexity of path enumeration and counting in weighted temporal graphs. In a weighted temporal graph, each edge has an availability time, a traversal time and some real cost. We introduce two bicriteria temporal min-cost…
We show how to represent sets in a linear space data structure such that expressions involving unions and intersections of sets can be computed in a worst-case efficient way. This problem has applications in e.g. information retrieval and…
In this paper, we address the weighted linear matroid intersection problem from the computation of the degree of the determinants of a symbolic matrix. We show that a generic algorithm computing the degree of noncommutative determinants,…
The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge…