Computational Bounds on Hierarchical Data Processing with Applications to Information Security

Motivated by the study of algorithmic problems in the domain of information security, in this paper, we study the complexity of a new class of computations over a collection of values associated with a set of n elements. We introduce hierarchical data processing (HDP) problems which involve the computation of a collection of output values from an input set of n elements, where the entire computation is fully described by a directed acyclic graph (DAG). That is, individual computations are performed and intermediate values are processed according to the hierarchy induced by the DAG. We present an Ω(log n) lower bound on various computational cost measures for HDP problems. Essential in our study is an analogy that we draw between the complexities of any HDP problem of size n and searching by comparison in an order set of n elements, which shows an interesting connection between the two problems. In view of the logarithmic lower bounds, we also develop a new randomized DAG scheme for ...

• Type: Conference
• Year: 2005
• Where: ICALP
• Authors: Roberto Tamassia, Nikos Triandopoulos
• Keywords: Hdp Problems, ICALP 2005, Logarithmic Lower Bounds, Lower Bounds, Theoretical Computer Science