Related papers: Stabbing Planes
The Angular Constrained Minimum Spanning Tree Problem ($\alpha$-MSTP) is defined in terms of a complete undirected graph $G=(V,E)$ and an angle $\alpha \in (0,2\pi]$. Vertices of $G$ define points in the Euclidean plane while edges, the…
We study approaches for the exact solution of the \NP--hard minimum spanning tree problem under conflict constraints. Given a graph $G(V,E)$ and a set $C \subset E \times E$ of conflicting edge pairs, the problem consists of finding a…
We study rectangle stabbing problems in which we are given $n$ axis-aligned rectangles in the plane that we want to stab, i.e., we want to select line segments such that for each given rectangle there is a line segment that intersects two…
We present an engineered version of the divide-and-conquer algorithm for finding the closest pair of points, within a given set of points in the XY-plane. For this version of the algorithm we show that only two pairwise comparisons are…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
We introduce a simple yet effective sampling-based planner that is tailored for bottleneck pathfinding: Given an implicitly-defined cost map $\mathcal{M}:\mathbb{R}^d\rightarrow \mathbb{R}$, which assigns to every point in space a real…
Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
Symmetry breaking has been proven to be an efficient preprocessing technique for satisfiability solving (SAT). In this paper, we port the state-of-the-art SAT symmetry breaker BreakID to answer set programming (ASP). The result is a…
We propose a Branch-and-Cut (B&C) method for solving general MAP-MRF inference problems. The core of our method is a very efficient bounding procedure, which combines scalable semidefinite programming (SDP) and a cutting-plane method for…
We propose Splinter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic-based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants…
We study the MaxRes rule in the context of certifying unsatisfiability. We show that it can be exponentially more powerful than tree-like resolution, and when augmented with weakening (the system MaxResW), p-simulates tree-like resolution.…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…
Given a real algebraic curve, embedded in projective space, we study the computational problem of deciding whether there exists a hyperplane meeting the curve in real points only. More generally, given any divisor on such a curve, we may…
The incorporation of cutting planes within the branch-and-bound algorithm, known as branch-and-cut, forms the backbone of modern integer programming solvers. These solvers are the foremost method for solving discrete optimization problems…
For several decades the dominant techniques for integer linear programming have been branching and cutting planes. Recently, several authors have developed core point methods for solving symmetric integer linear programs (ILPs). An integer…
Any stretching of Ringel's non-Pappus pseudoline arrangement when projected into the Euclidean plane, implicitly contains a particular arrangement of nine triangles. This arrangement has a complex constraint involving the sines of its…
We present subquadratic algorithms in the algebraic decision-tree model for several \textsc{3Sum}-hard geometric problems, all of which can be reduced to the following question: Given two sets $A$, $B$, each consisting of $n$ pairwise…
This paper presents a new technique for data slicing of distributed programs running on a hierarchy of machines. Data slicing can be realized as a program transformation that partitions heaps of machines in a hierarchy into independent…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…