1introduction:some representative problems/引言:某些有代表的问题1 1.1a first problem:stable matching/个问题:稳定匹配1 1.2five representative problems/五个有代表的问题12 solvedexercises/带解答的练19 exercises/练22 notesand further rea/注释和进一步阅读28 2basics of algorithm analysis/算法分析基础29 2.1putational tractability/计算可解29 2.2asymptotic order of growth/增长的渐近阶35 2.3implementing the stable matching algorithm using lists and arrays/用列表和数组实现稳定匹配算法42 2.4a survey of mon running times/常用运行时间概述47 2.5a more plex data structure:priority queues/更复杂的数据结构:优先队列57 solvedexercises/带解答的练65 exercises/练67 notesand further rea/注释和进一步阅读70 3graphs/图73 3.1basic definitions and applications/基本定义与应用73 3.2graph connectivity and graph traversal/图的连通与图的遍历78 3.3implementing graph traversal using queues and stacks/用优先队列与栈实现图的遍历87 3.4testing bipartiteness:an application of breadth-first search/二分测试:宽度优先搜索的应用94 3.5connectivity in directed graphs/有向图中的连通97 3.6directed acyclic graphs and topological ordering/有向无环图与拓扑排序99 solvedexercises/带解答的练104 exercises/练107 notesand further rea/注释和进一步阅读112 4greedy algorithms/贪心算法115 4.1interval scheduling:the greedy algorithm stays ahead/区间调度:贪心算法领先116 4.2scheduling to minimize lateness:an exchange argument/小延迟调度:交换论证125 4.3optimal caching:a more plex exchange argument/优高速缓存:更复杂的交换论证131 4.4shortest paths in a graph/图的短路径137 4.5the minimum spanning tree problem/小生成树问题142 4.6implementing kruskal’s algorithm:the union-find data structure/实现kruskal算法:union-find数据结构151 4.7clustering/聚类157 4.8huffman codes and data pression/赫夫曼码与数据压缩161 4.9 minimum-cost arborescences:a multi-phase greedy algorithm/小费用有向树:多阶段贪心算法177 solvedexercises/带解答的练183 exercises/练188 notesand further rea/注释和进一步阅读205 5divide and conquer/分治策略209 5.1a first recurrence:the mergesort algorithm/个递推式:归并排序算法210 5.2further recurrence relations/更多的递推关系214 5.3counting inversions/逆序221 5.4fin the closest pair of points/找接邻近的点对225 5.5integer multiplication/整数乘法231 5.6convolutions and the fast fourier transform/卷积与快速傅里叶变换234 solvedexercises/带解答的练242 exercises/练246 notesand further rea/注释和进一步阅读249 6dynamic programming/动态规划251 6.1weighted interval scheduling:a recursive procedure/带权的区间调度:递归过程252 6.2principles of dynamic programming:memoization or iteration over subproblems/动态规划:备忘录或者子问题迭代258 6.3segmented least squares:multi-way choices/分段的小二乘:多重选择261 6.4subset sums and knaacks:ad a variable/子集和与背包:加一个变量266 6.5rna secondary structure:dynamic programming over intervals/rna二级结构:在区间上的动态规划272 6.6sequence alignment/序列比对278 6.7sequence alignment in linear space via divide and conquer/通过分治策略在线空间的序列比对284 6.8shortest paths in a graph/图中的短路径290 6.9shortest paths and distance vector protocols/短路径和距离向量协议297 6.10 cycles in a graph/图中的负圈301 solvedexercises/带解答的练307 exercises/练312 notesand further rea/注释和进一步阅读335 7work flow/网络流337 7.1the mamum-flow problem and the ford-fulkerson algorithm/优选流问题与ford-fulkerson算法338 7.2mamum flows and minimum cuts in a work/网络中的优选流与小割346 7.3choosing good augmenting paths/选择好的增广路径352 7.4 the preflow-push mamum-flow algorithm/前向流推动优选流算法357 7.5a first application:the bipartite matching problem/个应用:二分匹配问题367 7.6disjoint paths in directed and undirected graphs/有向与无向图中的不交路径373 7.7extensions to the mamum-flow problem/对优选流问题的推广378 7.8survey design/调查设计384 7.9airline scheduling/航线调度387 7.10image segmentation/图像分割391 7.11project selection/项目选择396 7.12baseball elimination/棒球排除400 7.13 a further direction:ad costs to the matching problem/进一步的方向:对匹配问题增加费用404 solvedexercises/带解答的练411 exercises/练415 notesand further rea/注释和进一步阅读448 8np and putational intractability/np与计算的难解451 8.1polynomial-time reductions/多项式时间归约452 8.2reductions via “gadgets”:the satisfiability problem/使用“零件”的归约:可满足问题459 8.3efficient certification and the definition of np/有效和np的定义463 8.4np-plete problems/np问题466 8.5sequencing problems/排序问题473 8.6partitioning problems/划分问题481 8.7graph coloring/图着485 8.8numerical problems/数值问题490 8.9co-np and the asymmetry of np/co-np及np的不对称495 8.10a partial taxonomy of hard problems/难问题的部分分类497 solvedexercises/带解答的练500 exercises/练505 notesand further rea/注释和进一步阅读529 9pace:a class of problems beyond np/pace:一类超出np的问题531 9.1pace/pace531 9.2some hard problems in pace/pace中的难问题533 9.3solving quantified problems and games in polynomial space/在多项式空间中解量化问题和博弈问题536 9.4solving the nning problem in polynomial space/在多项式空间内求解规划问题538 9.5proving problems pace-plete/证明问题是pace的543 solvedexercises/带解答的练547 exercises/练550 notesand further rea/注释和进一步阅读551 10exten the limits of tractability/扩展易解的界限553 10.1fin small vertex covers/找小的顶点覆盖554 10.2solving np-hard problems on trees/在树上解np难问题558 10.3coloring a set of circular arcs/圆弧集着563 10.4 tree deitions of graphs/图的树分解572 10.5 constructing a tree deition/构造树分解584 solvedexercises/带解答的练591 exercises/练594 notesand further rea/注释和进一步阅读598 11appromation algorithms/近似算法599 11.1greedy algorithms and bounds on the optimum:a load balancing problem/贪心算法与优值的界限:负载均衡问题600 11.2the center selection problem/中心选址问题606 11.3set cover:a general greedy heuristic/集合覆盖:一般的贪心启发式方法612 11.4the pricing method:vertex cover/定价法:顶点覆盖618 11.5mamization via the pricing method:the disjoint paths problem/用定价法优选化:不交路径问题624 11.6linear programming and roun:an application to vertex cover/线规划与舍入:对顶点覆盖的应用630 11.7 load balancing revisited:a more advanced lp application/再论负载均衡:更不错的lp应用637 11.8arbitrarily good appromations:the knaack problem/任意好的近似:背包问题644 solvedexercises/带解答的练649 exercises/练651 notesand further rea/注释和进一步阅读659 12local search/局部搜索661 12.1the landscape of an optimization problem/优化问题的地形图662 12.2the metropolis algorithm and simulated annealing/metropolis算法与模拟退火算法666 12.3an application of local search to hopfield neural works/局部搜索在hopfield神经网络中的应用671 12.4mamum-cut appromation via local search/局部搜索对优选割近似的应用676 12.5choosing a neior relation/选择邻居关系679 12.6 classification via local search/用局部搜索分类681 12.7best-response dynamics and nash equilibria/佳响应动态过程与纳什均衡690 solvedexercises/带解答的练700 exercises/练702 notesand further rea/注释和进一步阅读705 13randomized algorithms/算法707 13.1a first application:contention resolution/个应用:消除争用708 13.2fin the global minimum cut/求小割714 13.3random variables and their expectations/变量及其期望719 13.4a randomized appromation algorithm for max 3-sat/关于max 3-sat的近似算法724 13.5randomized divide and conquer:median-fin and quicksort/分治策略:求中位数与快速排序727 13.6hashing:a randomized implementation of dictionaries/散列法:字典的实现734 13.7fin the closest pair of points:a randomized approach/求邻近点对:方法741 13.8randomized caching/超高速缓存750 13.9chernoff bounds/切尔诺夫界758 13.10load balancing/负载均衡760 13.11packet routing/包路由选择762 13.12background:some basic probability definitions/背景:某些基本概率定义769 solvedexercises/带解答的练776 exercises/练782 notesand further rea/注释和进一步阅读793 epilogue:algorithms that run forever/后记:永不停止运行的算法795 references/参文献805
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