Maximum Matching in Bipartite Graphs
In many situations we are faced with a problem of pairing elements of two sets.…
Design & Analysis of Algorithms
Design & Analysis of Algorithms
The Simplex Method
We have already encountered linear programming (see Section 6.6)—the general problem of optimizing a linear…
Design & Analysis of Algorithms
Iterative Improvement
The greedy strategy, considered in the preceding chapter, constructs a solution to an optimization problem…
Design & Analysis of Algorithms
Huffman Trees and Codes
Suppose we have to encode a text that comprises symbols from some n-symbol alphabet by assigning…
Design & Analysis of Algorithms
Dijkstra’s Algorithm
In this section, we consider the single-source shortest-paths problem: for a given vertex called the source in a…
Design & Analysis of Algorithms
Kruskal’s Algorithm
In the previous section, we considered the greedy algorithm that “grows” a mini-mum spanning tree…
Design & Analysis of Algorithms
Prim’s Algorithm
The following problem arises naturally in many practical situations: given n points, connect them in the cheapest…
Design & Analysis of Algorithms
Greedy Technique
Let us revisit the change-making problem faced, at least subconsciously, by millions of cashiers all over the…
Design & Analysis of Algorithms
The Knapsack Problem and Memory Functions
We start this section with designing a dynamic programming algorithm for the knapsack problem: given n items…
Design & Analysis of Algorithms
Warshall’s and Floyd’s Algorithms
In this section, we look at two well-known algorithms: Warshall’s algorithm for computing the transitive…