pawe ł gawrychowski* and pat nicholson** *university of warsaw **max-planck-institut für...
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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