The price of anarchy in series-parallel graphs

Abstract Congestion games model self-interested agents competing for resources in communication networks. The price of anarchy quantifies the deterioration in performance in such games compared to the optimal solution. Recent research has shown that, when the social cost is defined as the maximum cost of all players, specific graph topologies impose a bound on the price of anarchy. We extend this research by providing bounds on the price of anarchy for congestion games on series-parallel networks. First we show that parallel composition does not increase the price of anarchy. This result is then used to show that the price of anarchy is bounded above by both the diameter of the graph and the number of players in the game, and that these bounds are tight. Finally we identify an important aspect of proofs for bounds on the price of anarchy: when a bound is achieved by restricting multiple parameters of the game, one should also prove that this bound cannot be realized using only a subset of these restrictions

Delta lake: high-performance ACID table storage over cloud object stores

Cloud object stores such as Amazon S3 are some of the largest and most cost-effective storage systems on the planet, making them an attractive target to store large data warehouses and data lakes. Unfortunately, their implementation as key-value stores makes it difficult to achieve ACID transactions and high performance: metadata operations such as listing objects are expensive, and consistency guarantees are limited. In this paper, we present Delta Lake, an open source ACID table storage layer over cloud object stores initially developed at Databricks. Delta Lake uses a transaction log that is compacted into Apache Parquet format to provide ACID properties, time travel, and significantly faster metadata operations for large tabular datasets (e.g., the ability to quickly search billions of table partitions for those relevant to a query). It also leverages this design to provide high-level features such as automatic data layout optimization, upserts, caching, and audit logs. Delta Lake tables can be accessed from Apache Spark, Hive, Presto, Redshift and other systems. Delta Lake is deployed at thousands of Databricks customers that process exabytes of data per day, with the largest instances managing exabyte-scale datasets and billions of objects

Delta lake: high-performance ACID table storage over cloud object stores

Cloud object stores such as Amazon S3 are some of the largest and most cost-effective storage systems on the planet, making them an attractive target to store large data warehouses and data lakes. Unfortunately, their implementation as key-value stores makes it difficult to achieve ACID transactions and high performance: metadata operations such as listing objects are expensive, and consistency guarantees are limited. In this paper, we present Delta Lake, an open source ACID table storage layer over cloud object stores initially developed at Databricks. Delta Lake uses a transaction log that is compacted into Apache Parquet format to provide ACID properties, time travel, and significantly faster metadata operations for large tabular datasets (e.g., the ability to quickly search billions of table partitions for those relevant to a query). It also leverages this design to provide high-level features such as automatic data layout optimization, upserts, caching, and audit logs. Delta Lake tables can be accessed from Apache Spark, Hive, Presto, Redshift and other systems. Delta Lake is deployed at thousands of Databricks customers that process exabytes of data per day, with the largest instances managing exabyte-scale datasets and billions of objects