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merge-sort divide-and-conquer comparison-sort stable-sort quick-sort quick-select partition randomized heapsort heap priority-queue in-place-sort algorithm-analysis monty-hall probability monte-carlo bayes conditional-probability ABA-problem lock-free CAS concurrency atomic memory-model set-cover approximation greedy LP-rounding NP-hard dual-fitting randomized-rounding primal-dual graph adjacency-matrix CSR sparse-matrix data-structure kronecker-product linear-algebra tensor combinatorics CUDA GPU parallel-computing C++ stream memory-management knapsack FPTAS dynamic-programming k-center clustering metric PTAS algorithm-families MPI distributed-computing HPC message-passing PageRank BFS minimum-degree-spanning-tree spanning-tree linear-programming LP simplex optimization duality scheduling completion-time weighted-job network-flow flow-decomposition circulation chernoff-bounds concentration-inequality multicommodity-flow congestion survivable-network-design connectivity LP-duality complementary-slackness facility-location steiner-tree semidefinite-programming SDP convex-optimization MAX-CUT graph-coloring markov-inequality expectation chromatic-number harmonic-series geometric-series mathematical-tools summation tree-metrics metric-approximation metric-embedding buy-at-bulk network-design hardness-of-approximation MAX-SAT PCP-theorem inapproximability insertion-sort introduction sorting Big-O time-complexity space-complexity amortized-analysis array linked-list dynamic-array stack queue LIFO FIFO beatty-theorem rayleigh-theorem number-theory irrational-numbers floor-function beatty-sequence fibonacci matrix-exponentiation recurrence closed-form master-theorem maximum-subarray kadane BigInteger NTT Karatsuba ArbitraryPrecision polynomial-multiplication modular-arithmetic NP 3-SAT independent-set gadget P-vs-NP reduction bipartite-matching edmonds-karp capacity-scaling alternating-path memoization LNS sequence-alignment interval-scheduling EDD job-scheduling stay-ahead certifying-algorithm karatsuba integer-multiplication closest-pair ford-fulkerson max-flow-min-cut augmenting-path residual-graph NP-complete 3DM cook-levin nondeterminism complexity-theory polynomial-reduction vertex-cover RNA-folding bellman-ford shortest-path negative-edges