A Deamortization Approach for Dynamic Spanner and Dynamic Maximal Matching

Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For this reason, there exist many recent randomized results that aim provide guarantee expected. The strongest possible algorithm is it always correct (Las Vegas) and high-probability which gives bound on the time holds with high probability. In article, we present first polylogarithmic bounds spanner maximal matching problem. (1) spanner, only known o ( n ) were O 3/4 maintaining 3-spanner 5/9 5-spanner. We give k log 3 2k-1 )-spanner, yields polylog all constant . (All above maintain optimal tradeoff of stretch Õ( 1+1/k edges.) (2) matching, or 2-approximate maximum no o(n) was (log 5 )) time; similar existed (2+?)-approximate, hence maximal. Our achieved using new approach converting guarantees ones by going through third type guarantee, middle ground between two above: An said expected ? if every ?, process ? at most ?. Although expected, does resolve fundamental problem amortization: A O(1) still allows possibility 1/ f(n) updates requires ? process, arbitrarily black-box reduction converts any structure into one time: query remains same, while increases factor 2(n) ). Thus, achieve our in steps: First, show how convert existing running times times. Then, use bound. All Las-Vegas-type algorithms.