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.Expand

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.Expand

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… Expand

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… Expand

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).Expand

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.Expand

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.Expand

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.Expand

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.Expand