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Unformatted text preview: ∑ v i i ∈ F Earliest fnish time will not work (Greedy algorithms won’t work) Solved by dynamic programming “Greedy stays ahead without the greediness.” ±or t = 0, 1, 2, . .., T fnd the best schedule ±or the subinterval end±or (3) Maximum Matching Input. A bipartite graph Output. A matching (a set o± edges with distinct vertices) o± maximum cardinality 6-2 Solution uses max-f ow (4) Maximum independent set Input: An undirected graph G = (GE) Output: An independent set oF max cardinality (set oF vertices with no edge between them) Brute ±orce: O(k 2 n 2 ) Best known O(n 0.79. ..k + O(1) ) Poly-time algo? Equiv’t P = NP (5) Competitive Facility Location: Input: A graph with vertex weights w i ≥ A: 15 + 10 B: 10 Does player B have a strategy that guarantees ≥ p points? PSPACE-hard 6-3...
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