Algorithms in a Nutshell

(^152) | Chapter 6: Graph Algorithms Solution A sample C++ solution is shown in Example 6-2. BREADTH-FIRSTSEARCHstores its state ...

Single-Source Shortest Path | 153 Graph Algorithms Since the queue can add and remove elements in constant time, the cost of man ...

(^154) | Chapter 6: Graph Algorithms We assume that no arithmetic overflow occurs in line 12 of Figure 6-13; should you be conce ...

Single-Source Shortest Path | 155 Graph Algorithms Solution As DIJKSTRA’SALGORITHMexecutes,dist[v]represents the maximum length ...

(^156) | Chapter 6: Graph Algorithms Consequences Arithmetic error also may occur if the sum of the individual edge weights exce ...

Single-Source Shortest Path | 157 Graph Algorithms We can further optimize Example 6-4 to remove all of the C++ standard templat ...

(^158) | Chapter 6: Graph Algorithms Figure 6-15. Dijkstra’s Algorithm for dense graphs fact sheet Example 6-5. Optimized Dijkst ...

Single-Source Shortest Path | 159 Graph Algorithms Variations Ifashortestflightpathhasmanyhops,youmightbesolvingthewrongproblem. ...

(^160) | Chapter 6: Graph Algorithms In this presentation we tried to minimize the distance traversed. In other applica- tions w ...

Single-Source Shortest Path | 161 Graph Algorithms Intuitively BELLMAN-FORDoperates by makingnsweeps over a graph that check to ...

(^162) | Chapter 6: Graph Algorithms Benchmark data It is difficult to generate “random graphs.” In Table 6-2, we show the perfo ...

Single-Source Shortest Path | 163 Graph Algorithms Figure 6-17. Different executions of Bellman-Ford have the same result Table ...

(^164) | Chapter 6: Graph Algorithms Dense graphs For dense graphs,Eis on the order of O(V^2 ); for example, in a complete graph ...

All Pairs Shortest Path | 165 Graph Algorithms All Pairs Shortest Path Instead of finding the shortest path from a single source ...

(^166) | Chapter 6: Graph Algorithms For values ofk>0, we assume when computingdistkthat we have already computeddistk–1(in d ...

All Pairs Shortest Path | 167 Graph Algorithms If it does not, the result of our previous computation,distk–1[i][j], is still o ...

(^168) | Chapter 6: Graph Algorithms FLOYD-WARSHALL computes adist[i][j] matrix that stores the resulting computations of the sh ...

Minimum Spanning Tree Algorithms | 169 Graph Algorithms Minimum Spanning Tree Algorithms Given an undirected, connected graphG=( ...

(^170) | Chapter 6: Graph Algorithms Consequences For dense graphs, the priority queue can be implemented instead with a Fibonac ...

References | 171 Graph Algorithms References Cormen, Thomas H., Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Intr ...