Pawe ł Gawrychowski* and Pat Nicholson** *University of Warsaw **Max-Planck-Institut für Informatik

Range Queries in Arrays

Encoding Range Queries in Arrays

Typical Data Structure Input Data (Relatively Big) Input Data (Relatively Big)

Typical Data Structure Input Data (Relatively Big) Input Data (Relatively Big) Data Structure Preprocess

Encoding Approach Input Data (Relatively Big) Input Data (Relatively Big)

Encoding Approach Input Data (Relatively Big) Input Data (Relatively Big) Preprocess w.r.t. Some Query Encoding (Hope: much smaller)

Encoding Approach Input Data (Relatively Big) Input Data (Relatively Big) Preprocess w.r.t. Some Query Encoding (Hope: much smaller)

Encoding Approach Input Data (Relatively Big) Input Data (Relatively Big) Preprocess w.r.t. Some Query Encoding (Hope: much smaller) Auxiliary Data Structures: (Should be smaller still)

Encoding Approach Succinct Data Structure: Minimum Space Possible Encoding (Hope: much smaller) Auxiliary Data Structures: (Should be smaller still) Input Data (Relatively Big) Input Data (Relatively Big) Preprocess w.r.t. Some Query

Encoding Approach Succinct Data Structure: Minimum Space Possible Encoding (Hope: much smaller) Auxiliary Data Structures: (Should be smaller still) Query (Hope: as fast as non- succinct counterpart) Input Data (Relatively Big) Input Data (Relatively Big) Preprocess w.r.t. Some Query

This Talk: Maximum-Sum Segments

Range Maximum-Sum Segment Queries

Now find the minimum in this range

Candidate Pairs

What 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 Good ()((())(()(()))())((()(()))())

Recall The Query Algorithm

Problem: cannot store the left siblings explicitly

Idea: try to find something that is nested

What Do We Store?