7 research outputs found
Cache-oblivious dynamic dictionaries with update/query tradeoffs
Get PDFSeveral existing cache-oblivious dynamic dictionaries
achieve O(logB N) (or slightly better O(logB
N over M )) memory
transfers per operation, where N is the number of
items stored, M is the memory size, and B is the
block size, which matches the classic B-tree data structure.
One recent structure achieves the same query
bound and a sometimes-better amortized update bound
of O (...) memory transfers.
This paper presents a new data structure, the xDict,
implementing predecessor queries in O(...)worstcase
memory transfers and insertions and deletions in
O (...) amortized memory transfers, for any constant " with 0 < epsilon < 1. For example, the xDict achieves subconstant amortized update cost when N = ..., whereas the B-tree’s ... is subconstant only when ... is subconstant only when N = .... The xDict attains the optimal tradeoff between insertions and queries, even in the broader external-memory model, for the range where inserts cost between (...) and O(1= lg3 N) memory transfers.Danish National Research Foundation (MADALGO (Center for Massive Data Algorithmics))National Science Foundation (U.S.) (NSF Grants CCF-0541209)National Science Foundation (U.S.) (NSF Grants CCF-0541209)Computing Innovation Fellow
Approximate Dictionary Queries
No full text. Given a set of n binary strings of length m each. We consider the problem of answering d--queries. Given a binary query string ff of length m, a d--query is to report if there exists a string in the set within Hamming distance d of ff. We present a data structure of size O(nm) supporting 1--queries in time O(m) and the reporting of all strings within Hamming distance 1 of ff in time O(m). The data structure can be constructed in time O(nm). A slightly modified version of the data structure supports the insertion of new strings in amortized time O(m). 1 Introduction Let W = fw 1 ; : : : ; wng be a set of n binary strings of length m each, i.e. w i 2 f0; 1g m . The set W is called the dictionary. We are interested in answering d-- queries, i.e. for any query string ff 2 f0; 1g m to decide if there is a string w i in W with at most Hamming distance d of ff. Minsky and Papert originally raised this problem in [12]. Recently a sequence of papers have considered how to solve thi..
Optimal sparse matrix dense vector multiplication in the I/O-model
No full textWe analyze the problem of sparse-matrix dense-vector multiplication (SpMV) in the I/O model. In the SpMV, the objective is to compute y = Ax, where A is a sparse matrix and x and y are vectors. We give tight upper and lower bounds on the number of block transfers as a function of the sparsity k, the number of nonzeros in a column of A. Parameter k is a knob that bridges the problems of permuting (k = 1) and dense matrix multiplication (k = N). When the nonzero elements of A are stored in column-major order, SpMV takes O mi
