Polynomial-Time Algorithms for Energy Games with - ALGO 2012 PDF
Preview Polynomial-Time Algorithms for Energy Games with - ALGO 2012
Polynomial-Time Algorithms for Energy Games with Special Weight Structures Krishnendu Chatterjee1 Monika Henzinger2 Sebastian Krinninger2 Danupon Nanongkai2 1ISTAustria 2UniversityofVienna ESA 2012 1/13 Energy games Rules: Bob Integer-weighted, directed graph 3 Car is moved along graph Energy of car can increase or decrease (weights) 4 Two players: Alice and Bob owning nodes 7 -2 Owner may choose next edge -2 -8 (= strategy) Alice wins at starting node if Alice energy always ≥ 0 Otherwise Alice loses Question Least initial energy ∈ [0,∞] s.t. Alice can win? 2/13 Energy games Rules: Bob Integer-weighted, directed graph 3 Car is moved along graph Energy of car can increase or decrease (weights) 4 Two players: Alice and Bob owning nodes 7 -2 Owner may choose next edge -2 -8 (= strategy) Alice wins at starting node if Alice energy always ≥ 0 Otherwise Alice loses Initial energy level: 5 Question Least initial energy ∈ [0,∞] s.t. Alice can win? 2/13 Energy games Rules: Bob Integer-weighted, directed graph 3 Car is moved along graph Energy of car can increase or decrease (weights) 4 Two players: Alice and Bob owning nodes 7 -2 Owner may choose next edge -2 -8 (= strategy) Alice wins at starting node if Alice energy always ≥ 0 Otherwise Alice loses Energy level: 3 Question Least initial energy ∈ [0,∞] s.t. Alice can win? 2/13 Energy games Rules: Bob Integer-weighted, directed graph 3 Car is moved along graph Energy of car can increase or decrease (weights) 4 Two players: Alice and Bob owning nodes 7 -2 Owner may choose next edge -2 -8 (= strategy) Alice wins at starting node if Alice energy always ≥ 0 Otherwise Alice loses Energy level: 3 Question Least initial energy ∈ [0,∞] s.t. Alice can win? 2/13 Energy games Rules: Bob Integer-weighted, directed graph 3 Car is moved along graph Energy of car can increase or decrease (weights) 4 Two players: Alice and Bob owning nodes 7 -2 Owner may choose next edge -2 -8 (= strategy) Alice wins at starting node if Alice energy always ≥ 0 Otherwise Alice loses Energy level: −5 Question Least initial energy ∈ [0,∞] s.t. Alice can win? 2/13 Energy games Rules: Bob Integer-weighted, directed graph 3 Car is moved along graph Energy of car can increase or decrease (weights) 4 Two players: Alice and Bob owning nodes 7 -2 Owner may choose next edge -2 -8 (= strategy) Alice wins at starting node if Alice energy always ≥ 0 Otherwise Alice loses Initial energy level: 5 Question Least initial energy ∈ [0,∞] s.t. Alice can win? 2/13 Energy games Rules: Bob Integer-weighted, directed graph 3 Car is moved along graph Energy of car can increase or decrease (weights) 4 Two players: Alice and Bob owning nodes 7 -2 Owner may choose next edge -2 -8 (= strategy) Alice wins at starting node if Alice energy always ≥ 0 Otherwise Alice loses Energy level: 12 Question Least initial energy ∈ [0,∞] s.t. Alice can win? 2/13 Energy games Rules: Bob Integer-weighted, directed graph 3 Car is moved along graph Energy of car can increase or decrease (weights) 4 Two players: Alice and Bob owning nodes 7 -2 Owner may choose next edge -2 -8 (= strategy) Alice wins at starting node if Alice energy always ≥ 0 Otherwise Alice loses Energy level: 12 Question Least initial energy ∈ [0,∞] s.t. Alice can win? 2/13 Energy games Rules: Bob Integer-weighted, directed graph 3 Car is moved along graph Energy of car can increase or decrease (weights) 4 Two players: Alice and Bob owning nodes 7 -2 Owner may choose next edge -2 -8 (= strategy) Alice wins at starting node if Alice energy always ≥ 0 Otherwise Alice loses Energy level: 16 Question Least initial energy ∈ [0,∞] s.t. Alice can win? 2/13
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