For any odd integer q > 1, we improve the lower bound for general q-query locally decodablecodes C : {0, 1}n → {0, 1}m from m = Ω(n/ logn)q+1q−1 to m = Ω( nq+1q−1) / logn. For example,for q = 3 we improve the previous bound from Ω(n/ log n) to Ω(n/ logn). For linear 3-querylocally decodable codes C : F → F, we improve the lower bound further to Ω(n/ log log n...

We study common query intentions in a software developer network with more than one million users. Based on a large query log analysis we could identify typical search intentions and identify common entities. For resolving most frequent query intentions and to identify entities and relationships from relevant pages we recommend state-of-the-art information extraction technologies.

Let G = (V,E) be a finite graph, and f : V → N be any function. The Local Search problem consists in finding a local minimum of the function f on G, that is a vertex v such that f(v) is not larger than the value of f on the neighbors of v in G. In this note, we first prove a separation theorem slightly stronger than the one of Gilbert, Hutchinson and Tarjan for graphs of constant genus. This re...

Given a string of length n that is composed of r runs of letters from the alphabet {0, 1, . . . , σ−1} such that 2 ≤ σ ≤ r, we describe a data structure that, provided r ≤ n/ log n, stores the string in r log nσ r + o(r log nσ r ) bits and supports select and access queries in O(log log(n/r) log logn ) time and rank queries in O(log log(nσ/r) log logn ) time. We show that r log n(σ−1) r bits ar...

We consider a central problem in text indexing: Given a text T over an alphabet Σ, construct a compressed data structure answering the queries char (i), rank s(i), and selects(i) for a symbol s ∈ Σ. Many data structures consider these queries for static text T [GGV03, FM01, SG06, GMR06]. We consider the dynamic version of the problem, where we are allowed to insert and delete symbols at arbitra...

In this paper we consider solutions to the static dictionary problem on ACo RAMs, i.e. random access machines where the only restriction on theJinite instruction set is that all computationcil instructions are in ACO. Our main result is a tight upper and lower bound of 0 (Jlog n / log log n ) on the time for (answering membership queries in a set of size n when reasonable space is used for the ...

We study the $k$ nearest neighbors problem in plane for general, convex, pairwise disjoint sites of constant description complexity such as line segments, disks, and quadrilaterals under a general family distance functions including $L_p$ norms additively weighted Euclidean distances. compose static data structure this setting with nearly optimal $O(n\log\log n)$ space, $O(\log n+k)$ query time...

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log logn) time, point deletions in amortized O(log n · log logn) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requi...

In this paper we consider solutions to the dictionary problem on AC RAMs, i.e. random access machines where the only restriction on the finite instruction set is that all computational instructions are in AC. Our main result is a tight upper and lower bound of Θ( √ log n/ log log n) on the time for answering membership queries in a set of size n when reasonable space is used for the data struct...