External memory priority queues with decrease-key and applications to graph algorithms

We present priority queues in the external memory model with block size B and main memory size M that support on N elements, operation Update (a combination of operations Insert and DecreaseKey) in O(1/Blog_{M/B} N/B) amortized I/Os and operations ExtractMin and Delete in O(ceil[(M^epsilon)/B log_{M/B} N/B] log_{M/B} N/B) amortized I/Os, for any real epsilon in (0,1), using O(N/Blog_{M/B} N/B) blocks. Previous I/O-efficient priority queues either support these operations in O(1/Blog_2 N/B) amortized I/Os [Kumar and Schwabe, SPDP \u2796] or support only operations Insert, Delete and ExtractMin in optimal O(1/Blog_{M/B} N/B) amortized I/Os, however without supporting DecreaseKey [Fadel et al., TCS \u2799]. We also present buffered repository trees that support on a multi-set of N elements, operation Insert in O(1/Blog_M/B N/B) I/Os and operation Extract on K extracted elements in O(M^{epsilon} log_M/B N/B + K/B) amortized I/Os, using O(N/B) blocks. Previous results achieve O(1/Blog_2 N/B) I/Os and O(log_2 N/B + K/B) I/Os, respectively [Buchsbaum et al., SODA \u2700]. Our results imply improved O(E/Blog_{M/B} E/B) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs (V,E) with E = Omega (V^(1+epsilon)), epsilon > 0 and V = Omega (M), which is equal to the I/O-optimal bound for sorting E values in external memory

External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms

We present priority queues in the external memory model with block size B and main memory size M that support on N elements, operation Update (a combination of operations Insert and DecreaseKey) in O(1/Blog_{M/B} N/B) amortized I/Os and operations ExtractMin and Delete in O(ceil[(M^epsilon)/B log_{M/B} N/B] log_{M/B} N/B) amortized I/Os, for any real epsilon in (0,1), using O(N/Blog_{M/B} N/B) blocks. Previous I/O-efficient priority queues either support these operations in O(1/Blog_2 N/B) amortized I/Os [Kumar and Schwabe, SPDP \u2796] or support only operations Insert, Delete and ExtractMin in optimal O(1/Blog_{M/B} N/B) amortized I/Os, however without supporting DecreaseKey [Fadel et al., TCS \u2799]. We also present buffered repository trees that support on a multi-set of N elements, operation Insert in O(1/Blog_M/B N/B) I/Os and operation Extract on K extracted elements in O(M^{epsilon} log_M/B N/B + K/B) amortized I/Os, using O(N/B) blocks. Previous results achieve O(1/Blog_2 N/B) I/Os and O(log_2 N/B + K/B) I/Os, respectively [Buchsbaum et al., SODA \u2700]. Our results imply improved O(E/Blog_{M/B} E/B) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs (V,E) with E = Omega (V^(1+epsilon)), epsilon > 0 and V = Omega (M), which is equal to the I/O-optimal bound for sorting E values in external memory

External memory priority queues with decrease-key and applications to graph algorithms

We present priority queues in the cache-oblivious external memory model with block size B and main memory size M that support on N elements, operation \textsc{UPDATE} (combination of \textsc{INSERT} and \textsc{DECREASEKEY}) in O(1BlogλBNB) amortized I/Os and operations \textsc{EXTRACT-MIN} and \textsc{DELETE} in O(⌈λεBlogλBNB⌉logλBNB) amortized I/Os, using O(NBlogλBNB) blocks, for a user-defined parameter λ∈[2,N] and any real ε∈(0,1). Our result improves upon previous I/O-efficient cache-oblivious and cache-aware priority queues [Chowdhury and Ramachandran, TALG 2018], [Brodal et al. SWAT 2004], [Kumar and Schwabe, SPDP 1996], [Arge et al. SICOMP 2007], [Fadel et al. TCS 1999].We also present buffered repository trees that support on a multi-set of N elements, operation \textsc{INSERT} in O(1BlogλBNB) I/Os and operation \textsc{EXTRACT} on K extracted elements in O(λεBlogλBNB+KB) amortized I/Os, using O(NB) blocks, improving previous cache-aware and cache-oblivious results [Arge et al. SICOMP '07], [Buchsbaum et al. SODA '00].In the cache-oblivious model, for λ=O(E/V), we achieve O(EBlogEVBEB) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs (V,E). Our algorithms are I/O-optimal for E/V=Ω(M) (and in the cache-aware setting for λ=O(M)).info:eu-repo/semantics/publishe