In this paper we study the problem of finding disjoint paths in graphs. Whereas for specific graphs many (almost) matching upper and lower bounds are known for the competitiveness of on-line path selection algorithms, much less is known about how well on-line algorithms can perform in the general setting. In several papers the expansion has been used to measure the performance of off-line and on-line algorithms in this field. We study a class of simple deterministic on-line algorithms and show that they achieve a competitive ratio that is asymptotically equal to the best possible competitive ratio that can be achieved by any deterministic on-line algorithm. For this we use a parameter caled routing number which allows more precise results than the expansion. Interestingly, our upper bound on the competitive ratio is even better than the best approximation ratio known for off-line algorithms. Furthermore, we show that a refined variant of the routing number allows to construct on-line algorithms with a competitive ratio that is for many graphs significantly below the best possible upper bound for deterministic on-line algorithms if only the routing number or expansion of a graph is known. We also show that our algorithms can be transformed into efficient algorithms for the related unsplittable flow problem.
机译:最大不相交路径问题的简单在线算法
机译:基于树立形象的最大不相交路径的新算法
机译:基于树相似度的最大不相交路径新算法
机译:用于最大不相交路径问题的简单在线算法
机译:最大边不相交路径问题的遗传算法及其对路由和波长分配问题的扩展。
机译:基于树状图的最大不相交路径的新算法
机译:最大不相交路径问题的简单在线算法