Stefan Hougardy
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View article: A 13/6-Approximation for Strip Packing via the Bottom-Left Algorithm
A 13/6-Approximation for Strip Packing via the Bottom-Left Algorithm Open
In the Strip Packing problem, we are given a vertical strip of fixed width and unbounded height, along with a set of axis-parallel rectangles. The task is to place all rectangles within the strip, without overlaps, while minimizing the hei…
View article: A near-complete resolution of the exponential-time complexity of k-opt for the traveling salesman problem
A near-complete resolution of the exponential-time complexity of k-opt for the traveling salesman problem Open
The $k$-opt algorithm is one of the simplest and most widely used heuristics for solving the traveling salesman problem. Starting from an arbitrary tour, the $k$-opt algorithm improves the current tour in each iteration by exchanging up to…
View article: Local elimination in the traveling salesman problem
Local elimination in the traveling salesman problem Open
Hougardy and Schroeder (WG 2014) proposed a combinatorial technique for pruning the search space in the traveling salesman problem, establishing that, for a given instance, certain edges cannot be present in any optimal tour. We describe a…
View article: Fast Approximation Algorithms for Euclidean Minimum Weight Perfect Matching
Fast Approximation Algorithms for Euclidean Minimum Weight Perfect Matching Open
We study the Euclidean minimum weight perfect matching problem for $n$ points in the plane. It is known that any deterministic approximation algorithm whose approximation ratio depends only on $n$ requires at least $Ω(n \log n)$ time. We p…
View article: The Bottom-Left Algorithm for the Strip Packing Problem
The Bottom-Left Algorithm for the Strip Packing Problem Open
The bottom-left algorithm is a simple heuristic for the Strip Packing Problem. It places the rectangles in the given order at the lowest free position in the strip, using the left most position in case of ties. Despite its simplicity, the …
View article: The $k$-Opt algorithm for the Traveling Salesman Problem has exponential running time for $k \ge 5$
The $k$-Opt algorithm for the Traveling Salesman Problem has exponential running time for $k \ge 5$ Open
The $k$-Opt algorithm is a local search algorithm for the Traveling Salesman Problem. Starting with an initial tour, it iteratively replaces at most $k$ edges in the tour with the same number of edges to obtain a better tour. Krentel (FOCS…
View article: Local elimination in the traveling salesman problem
Local elimination in the traveling salesman problem Open
Hougardy and Schroeder (WG 2014) proposed a combinatorial technique for pruning the search space in the traveling salesman problem, establishing that, for a given instance, certain edges cannot be present in any optimal tour. We describe a…
View article: The Approximation Ratio of the $k$-Opt Heuristic for the Euclidean Traveling Salesman Problem
The Approximation Ratio of the $k$-Opt Heuristic for the Euclidean Traveling Salesman Problem Open
The $k$-Opt heuristic is a simple improvement heuristic for the Traveling Salesman Problem. It starts with an arbitrary tour and then repeatedly replaces $k$ edges of the tour by $k$ other edges, as long as this yields a shorter tour. We w…
View article: A Fast Optimal Double Row Legalization Algorithm
A Fast Optimal Double Row Legalization Algorithm Open
In Placement Legalization, it is often assumed that (almost) all standard cells possess the same height and can therefore be aligned in cell rows, which can then be treated independently. However, this is no longer true for recent technolo…
View article: The Approximation Ratio of the 2-Opt Heuristic for the Euclidean Traveling Salesman Problem
The Approximation Ratio of the 2-Opt Heuristic for the Euclidean Traveling Salesman Problem Open
The 2-Opt heuristic is a simple improvement heuristic for the Traveling Salesman Problem. It starts with an arbitrary tour and then repeatedly replaces two edges of the tour by two other edges, as long as this yields a shorter tour. We wil…
View article: The Approximation Ratio of the 2-Opt Heuristic for the Euclidean Traveling Salesman Problem
The Approximation Ratio of the 2-Opt Heuristic for the Euclidean Traveling Salesman Problem Open
The 2-Opt heuristic is a simple improvement heuristic for the Traveling Salesman Problem. It starts with an arbitrary tour and then repeatedly replaces two edges of the tour by two other edges, as long as this yields a shorter tour. We wil…
View article: BonnCell: Automatic Cell Layout in the 7-nm Era
BonnCell: Automatic Cell Layout in the 7-nm Era Open
Multipatterning technology used in 7-nm technology and beyond imposes more and more complex design rules on the layout of cells. The often nonlocal nature of these new design rules is a great challenge not only for human designers but also…
View article: The Approximation Ratio of the 2-Opt Heuristic for the Metric Traveling Salesman Problem
The Approximation Ratio of the 2-Opt Heuristic for the Metric Traveling Salesman Problem Open
The 2-Opt heuristic is one of the simplest algorithms for finding good solutions to the metric Traveling Salesman Problem. It is the key ingredient to the well-known Lin-Kernighan algorithm and often used in practice. So far, only upper an…