Size Bounds and Algorithms for Conjunctive Regular Path Queries

Conjunctive regular path queries (CRPQs) are one of the core classes of queries over graph databases. They are join intensive, inheriting their structure from the relational setting, but they also allow arbitrary length paths to connect points that are to be joined. However, despite their popularity, little is known about what are the best algorithms for processing CRPQs. We focus on worst-case optimal algorithms, which are algorithms that run in time bounded by the worst-case output size of queries, and have been recently deployed for simpler graph queries with very promising results. We show that the famous bound on the number of query results by Atserias, Grohe and Marx can be extended to CRPQs, but to obtain tight bounds one needs to work with slightly stronger cardinality profiles. We also discuss what algorithms follow from our analysis. If one pays the cost for fully materializing graph queries, then the techniques developed for conjunctive queries can be reused. If, on the other hand, one imposes constraint on the working memory of algorithms, then worst-case optimal algorithms must be adapted with care: the order of variables in which queries are processed can have striking implications on the running time of queries

Cryptocurrency Mining Games with Economic Discount and Decreasing Rewards

In the consensus protocols used in most cryptocurrencies, participants called miners must find valid blocks of transactions and append them to a shared tree-like data structure. Ideally, the rules of the protocol should ensure that miners maximize their gains if they follow a default strategy, which consists on appending blocks only to the longest branch of the tree, called the blockchain. Our goal is to understand under which circumstances are miners encouraged to follow the default strategy. Unfortunately, most of the existing models work with simplified payoff functions, without considering the possibility that rewards decrease over time because of the game rules (like in Bitcoin), nor integrating the fact that a miner naturally prefers to be paid earlier than later (the economic concept of discount). In order to integrate these factors, we consider a more general model where issues such as economic discount and decreasing rewards can be set as parameters of an infinite stochastic game. In this model, we study the limit situation in which a miner does not receive a full reward for a block if it stops being in the blockchain. We show that if rewards are not decreasing, then miners do not have incentives to create new branches, no matter how high their computational power is. On the other hand, when working with decreasing rewards similar to those in Bitcoin, we show that miners have an incentive to create such branches. Nevertheless, this incentive only occurs when a miner controls a proportion of the computational power which is close to half of the computational power of the entire network