21. november 2017

Jacob Holm modtager Best Paper Award ved SODA’18

Best Paper Award

Sammen med Aaron Bernstein (Columbia University, USA) og Eva Rotenberg (DTU) får DIKU's ph.d.-studerende, Jacob Holm, tildelt en Best Paper Award ved ACM-SIAM Symposium on Discrete Algorithm (SODA’18) i New Orleans, USA for artiklen Online Bipartite Matching with Amortized O(log² n) Replacements.

SODA konferencen, som er årets førende algoritmebegivenhed, fokuserer på forskning relateret til effektive algoritmer og datastrukturer til diskrete problemer.

Jacob Holms artikel er en af de i alt 10 accepterede artikler ved SODA'18, der er forfattet eller medforfattet af medlemmer af DIKUs nye forskningscenter Basic Algorithms Research Copenhagen (BARC).

Arbejdet med artiklen er lavet mens Eva Rotenberg, der er medforfatter på artiklen, ligeledes var ph.d.-studerende på DIKU.


Jakob HolmIn the online bipartite matching problem with replacements, all the vertices on one side of the bipartition are given, and the vertices on the other side arrive one by one with all their incident edges. The goal is to maintain a maximum matching while minimizing the number of changes (replacements) to the matching. We show that the greedy algorithm that always takes the shortest augmenting path from the newly inserted vertex (denoted the SAP protocol) uses at most amortized O(log² n)  replacements per insertion, where n  is the total number of vertices inserted. This is the first analysis to achieve a polylogarithmic number of replacements for any replacement strategy, almost matching the Ω(log n)  lower bound. The previous best known strategy achieved amortized O(√n)  replacements [Bosek, Leniowski, Sankowski, Zych, FOCS 2014]. For the SAP protocol in particular, nothing better than then trivial O(n)  bound was known except in special cases.
Our analysis immediately implies the same upper bound of O(log² n)  reassignments for the capacitated assignment problem, where each vertex on the static side of the bipartition is initialized with the capacity to serve a number of vertices.
We also analyze the problem of minimizing the maximum server load. We show that if the final graph has maximum server load L , then the SAP protocol makes amortized O(min{L log² n, √n log n})  reassignments. We also show that this is close to tight because Ω(min{L, √n})  reassignments can be necessary.