ENCODING NEAREST LARGER VALUES Pat Nicholson* and Rajeev Raman** * MPII ** University of Leicester Input Data (Relatively Big) DJ VU: THE ENCODING APPROACH Input Data (Relatively Big) Preprocess w.r.t. Some Query Encoding (Hope: much smaller) Input Data (Relatively Big) Preprocess w.r.t. Some Query Encoding (Hope: much smaller) DJ VU: THE ENCODING APPROACH Input Data (Relatively Big) Preprocess w.r.t. Some Query Encoding (Hope: much smaller) Auxiliary Data Structures: (Should be smaller still) DJ VU: THE ENCODING APPROACH Succinct Data Structure: Minimum Space Possible Encoding (Hope: much smaller) Auxiliary Data Structures: (Should be smaller still) Input Data (Relatively Big) Preprocess w.r.t. Some Query DJ VU: THE 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) Preprocess w.r.t. Some Query DJ VU: THE ENCODING APPROACH NEAREST LARGER VALUES OVERVIEW: ENCODING NLV For all these results: space bound is optimal to within lower order terms DistinctProblemSpaceQNotes Yes Unidirectional Cartesian Tree Bidirectional Cartesian Tree Nondirectional NoUnidirectional [Fischer et al. 2009] Cartesian Tree Bidirectional [Fischer 2011] Schrder Trees (Navigate CSA) Nondirectional OVERVIEW: ENCODING NLV DistinctProblemSpaceQNotes Yes Unidirectional Cartesian Tree Bidirectional Cartesian Tree NondirectionalThis paper: NLV Tree NoUnidirectional [Fischer et al. 2009] Cartesian Tree Bidirectional [Fischer 2011] Schrder Trees (Navigate CSA) Nondirectional BIGGER PICTURE CARTESIAN TREES REVIEW We can rebuild him. We have the technology. NONDIRECTIONAL NLV TREE Tie breaking rule: break ties to by choosing the one to the right. TIEBREAKING MATTERS? Rule To the right To the smaller To the larger IDEA: COMPRESS RUNS DIGRESSION: PATH (OR CHAIN) COMPRESSION Degree two Degree one Terminal Subtree COMPRESSING CARTESIAN TREES W.R.T. NLVS Forget about whether it zigs or zags, just store # in prefix THE ENCODING SUB-OPTIMALITY EXAMPLES LOWER BOUND SKETCH CONCLUSIONS AND OPEN PROBLEMS THANK YOU