• Publications
  • Influence
Towards polynomial lower bounds for dynamic problems
  • M. Patrascu
  • Mathematics, Computer Science
    STOC '10
  • 5 June 2010
TLDR
This work describes a carefully-chosen dynamic version of set disjointness (the "multiphase problem"), and conjecture that it requires n^Omega(1) time per operation, and forms the first nonalgebraic reduction from 3SUM, which allows3SUM-hardness results for combinatorial problems.
Time-space trade-offs for predecessor search
TLDR
The first lower bound for an explicit problem which breaks this communication complexity barrier is given, and it is implied that van Emde Boas' classic data structure from [FOCS'75] is optimal in this case.
On the possibility of faster SAT algorithms
We describe reductions from the problem of determining the satisfiability of Boolean CNF formulas (CNF-SAT) to several natural algorithmic problems. We show that attaining any of the following bounds
Planning for Fast Connectivity Updates
  • M. Patrascu, M. Thorup
  • Computer Science
    48th Annual IEEE Symposium on Foundations of…
  • 21 October 2007
TLDR
A linear-space representation of graphs is described which enables us to determine how a batch of edge updates can impact the graph.
Orthogonal range searching on the RAM, revisited
We present a number of new results on one of the most extensively studied topics in computational geometry, orthogonal range searching. All our results are in the standard word RAM model: We present
Logarithmic Lower Bounds in the Cell-Probe Model
TLDR
A new technique for proving cell-probe lower bounds on dynamic data structures is developed, which enables an amortized randomized $\Omega(\lg n)$ lower bound per operation for several data structural problems on $n$ elements, including partial sums, dynamic connectivity among disjoint paths, and several other dynamic graph problems (by simple reductions).
Dynamic Integer Sets with Optimal Rank, Select, and Predecessor Search
  • M. Patrascu, M. Thorup
  • Computer Science
    IEEE 55th Annual Symposium on Foundations of…
  • 13 August 2014
TLDR
The most interesting aspect of the data structure is that it supports all the above operations in constant time for sets of size n = wO(1), which resolves a main open problem of Ajtai, Komlos, and Fredman.
The geometry of binary search trees
TLDR
It is shown that there exists an equal-cost online algorithm, transforming the conjecture of Lucas and Munro into the conjecture that the greedy algorithm is dynamically optimal, and achieving a new lower bound for searching in the BST model.
The Power of Simple Tabulation Hashing
TLDR
While this scheme is not even 4-independent, it provides many of the guarantees that are normally obtained via higher independence, for example, Chernoff-type concentration, min-wise hashing for estimating set intersection, and cuckoo hashing.
Counting inversions, offline orthogonal range counting, and related problems
TLDR
The new technique is quite simple: it performs a "vertical partitioning" of a trie (akin to van Emde Boas trees), and uses ideas from external memory to improve a long-standing previous bound of O(n, lg) that followed from Dietz's data structure.
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