A Method for Fast Leaderboard Calculations in Massive Online Game-Based Environments

Leaderboards and other game elements are present in many online environments, not just in videogames. When such environments have relatively few users, the implementation of those leaderboards is not usually a problem; however, that is no longer the case when they have dozens of thousands or more. For those situations we propose a method that is easy and cheap to implement. It is based on two particular data structures, a Self-Balanced Ordering Statistic Tree and a hash table, to perform proper leaderboard calculations in a fast and cheap way. More specifically, our proposal has O(log2⁡N) time complexity, whereas other approaches also based on in-memory data structures like linked lists have O(N), and others based on Hard Disk Drive operations like a relational database have O(Nlog2⁡N). Such improvement with regard to the other approaches is corroborated with experimental results for several scenarios, also presented in this paper.

On the complexity of the balanced vertex ordering problem

Graphs and Algorithms International audience We consider the problem of finding a balanced ordering of the vertices of a graph. More precisely, we want to minimise the sum, taken over all vertices v, of the difference between the number of neighbours to the left and right of v. This problem, which has applications in graph drawing, was recently introduced by Biedl et al. [Discrete Applied Math. 148:27―48, 2005]. They proved that the problem is solvable in polynomial time for graphs with maximum degree three, but NP-hard for graphs with maximum degree six. One of our main results is to close the gap in these results, by proving NP-hardness for graphs with maximum degree four. Furthermore, we prove that the problem remains NP-hard for planar graphs with maximum degree four and for 5-regular graphs. On the other hand, we introduce a polynomial time algorithm that determines whetherthere is a vertex ordering with total imbalance smaller than a fixed constant, and a polynomial time algorithm that determines whether a given multigraph with even degrees has an 'almost balanced' ordering.