Showing papers by "Rezaul Chowdhury published in 2006"

Cache-oblivious dynamic programming

Abstract: We present efficient cache-oblivious algorithms for several fundamental dynamic programs. These include new algorithms with improved cache performance for longest common subsequence (LCS), edit distance, gap (i.e., edit distance with gaps), and least weight subsequence. We present a new cache-oblivious framework called the Gaussian Elimination Paradigm (GEP) for Gaussian elimination without pivoting that also gives cache-oblivious algorithms for Floyd-Warshall all-pairs shortest paths in graphs and 'simple DP', among other problems.

The cache-oblivious gaussian elimination paradigm: theoretical framework and experimental evaluation

Abstract: The cache-oblivious Gaussian Elimination Paradigm (GEP) was introduced by the authors in [6] to obtain efficient cache-oblivious algorithms for several important problems that have algorithms with triply-nested loops similar to those that occur in Gaussian elimination. These include Gaussian elimination and LU-decomposition without pivoting, all-pairs shortest paths and matrix multiplication. In this paper, we prove several important properties of the cache-oblivious framework for GEP given in [6], which we denote by I-GEP. We build on these results to obtain C-GEP, a completely general cache-oblivious implementation of GEP that applies to any code in GEP form, and which has the same time and I/O bounds as the earlier algorithm in [6], while using a modest amount of additional space. We present an experimental evaluation of the caching performance of I-GEP and CGEP in relation to the traditional Gaussian elimination algorithm. Our experimental results indicate that I-GEP and C-GEP outperform GEP on inputs of reasonable size, with dramatic improvement in running time over GEP when the data is out of core. ‘Tiling’, an important loop transformation technique employed by optimizing compilers in order to improve temporal locality in nested loops, is a cache-aware method that does not adapt to all levels in a multi-level memory hierarchy. The cache-oblivious GEP framework (either I-GEP or C-GEP) produces system-independent I/O-efficient code for triply nested loops of the form that appears in Gaussian elimination without pivoting, and is potentially applicable to being used by optimizing compilers for loop transformation. ∗Department of Computer Sciences, University of Texas, Austin, TX 78712. Email: {shaikat,vlr}@cs.utexas.edu. This work was supported in part by NSF Grant CCF-0514876 and NSF CISE Research Infrastructure Grant EIA-0303609.

Brief announcement: The cache-oblivious Gaussian elimination paradigm -Theoretical framework and experimental evaluation

Abstract: Cache-efficient algorithms improve execution time by exploiting data parallelism inherent in the transfer of blocks of useful data between adjacent memory levels. By increasing locality in their memory access patterns, these algorithms try to keep the number of block transfers small. The cache-oblivious model [1] is a further refinement that enables the development of system-independent cache-efficient algorithms that simultaneously adapt to all levels of a multi-level memory hierarchy. This leads to fuller use of data parallelism and also produces portable code. The cache-oblivious model represents the memory hierarchy with two memory levels — an ideal cache of size M and an unlimited main memory partitioned into blocks of size B. The cache complexity of an algorithm is the number of I/Os (i.e., block transfers) performed between these two levels. In [2] we introduced the Gaussian Elimination Paradigm (GEP) — a cache-oblivious framework for several important problems solvable using a construct similar to the computation in Gaussian elimination without pivoting (see Fig. 1). The traditional GEP code in Fig. 1 runs in O n time and incurs O n 3