Abstract:Graph Crossing Number is a fundamental and extensively studied problem with wide ranging applications. In this problem, the goal is to draw an input graph G in the plane so as to minimize the number of crossings between the images of its edges. The problem is notoriously difficult, and despite extensive work, non-trivial approximation algorithms are only known for bounded-degree graphs. Even for this special case, the best current algorithm achieves a Õ( √ n)-approximation, while the best current negative resu… Show more
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