English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We provide exact and approximation methods for solving a geometric relaxationof the Traveling Salesman Problem (TSP) that occurs in curve reconstruction:for a given set of vertices in the plane, the problem Minimum Perimeter Polygon(MPP) asks for a (not necessarily simply connected) polygon with shortestpossible boundary length. Even though the closely related problem of finding aminimum cycle cover is polynomially solvable by matching techniques, we provehow the topological structure of a polygon leads to NP-hardness of the MPP. Onthe positive side, we show how to achieve a constant-factor approximation.  When trying to solve MPP instances to provable optimality by means of integerprogramming, an additional difficulty compared to the TSP is the fact that onlya subset of subtour constraints is valid, depending not on combinatorics, buton geometry. We overcome this difficulty by establishing and exploitingadditional geometric properties. This allows us to reliably solve a wide rangeof benchmark instances with up to 600 vertices within reasonable time on astandard machine. We also show that using a natural geometry-basedsparsification yields results that are on average within 0.5% of the optimum.

Computing Nonsimple Polygons of Minimum Perimeter