Cell Probe Lower Bounds for Succinct Data Structures

Encodings of Range Maximum-Sum Segment Queries and ApplicationsPawe Gawrychowski* and Pat Nicholson***University of Warsaw**Max-Planck-Institut fr InformatikRange Queries in ArraysEncoding Range Queries in ArraysTypical Data StructureInput Data(Relatively Big)Typical Data StructureInput Data(Relatively Big)Data StructurePreprocessEncoding ApproachInput Data(Relatively Big)Encoding ApproachInput Data(Relatively Big)Preprocessw.r.t.Some QueryEncoding(Hope: much smaller)Encoding ApproachInput Data(Relatively Big)Preprocessw.r.t.Some QueryEncoding(Hope: much smaller)Encoding ApproachInput Data(Relatively Big)Preprocessw.r.t.Some QueryEncoding(Hope: much smaller)Auxiliary Data Structures:(Should be smaller still)Encoding ApproachSuccinct Data Structure: Minimum Space PossibleEncoding(Hope: much smaller)Auxiliary Data Structures:(Should be smaller still)Input Data(Relatively Big)Preprocessw.r.t.Some QueryEncoding ApproachSuccinct Data Structure: Minimum Space PossibleEncoding(Hope: much smaller)Auxiliary Data Structures:(Should be smaller still)Query(Hope: as fast as non-succinct counterpart)

Input Data(Relatively Big)Preprocessw.r.t.Some QueryThis Talk: Maximum-Sum SegmentsRange Maximum-Sum Segment QueriesRange Maximum-Sum Segment Queries

Really similar to RMaxQ

Range Maximum-Sum Segment Queries

Now find the minimum in this range

Now find the minimum in this range

Candidate PairsWhat Do They Store?

How to answer a query: the easy case

How to answer a query: the not so easy case

Reducing the Space

Nested Is Good12345678()((())(()(()))())((()(()))())

Recall The Query Algorithm

Recall The Query Algorithm

Recall The Query Algorithm

Recall The Query Algorithm

Problem: cannot store the left siblings explicitly

Idea: try to find something that is nested

What Do We Store?Thank You