Communication Complexity with Synchronized Clocks

Abstract—We consider two natural extensions of the communication complexity model that are inspired by distributed computing. In both models, two parties are equipped with synchronized discrete clocks, and we assume that a bit can be sent from one party to another in one step of time. Both models allow implicit communication, by allowing the parties to choose whether to send a bit during each step. We examine trade-offs between time (total number of possible time steps elapsed) and communication (total number of bits actually sent). In the synchronized bit model, we measure the total number of bits sent between the two parties (e.g., email). We show that, in this model, communication costs can differ from the usual communication complexity by a factor roughly logarithmic in the number of time steps, and no more than such a factor. In the synchronized connection model, both parties choose whether or not to open their end of the communication channel at each time step. An exchange of b...

• Type: Conference
• Year: 2010
• Where: COCO
• Authors: Russell Impagliazzo, Ryan Williams
• Keywords: Algorithms, COCO 2010, Communication Complexity, Time Steps, Total Number