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Shrinking transistor sizes, increasing circuit complexities, and high clock frequencies bring new board-routing challenges that cannot be handled effectively by traditional routing algorithms. Many high-end designs in the industry today require manual routing efforts, which increases the design-cycle times considerably. In this paper, we propose an escape-routing algorithm to route nets within multiple dense components simultaneously so that the number of crossings in the intermediate area is minimized. We also show how to handle high-speed-design constraints within the framework of this algorithm. Experimental comparisons with a recently proposed algorithm show that our algorithm reduces the via requirements of industrial test cases on average by 39%.