Further Connections between Contract-Scheduling and Ray-Searching - PowerPoint PPT Presentation

Further Connections between Contract-Scheduling and Ray-Searching Problems Spyros Angelopoulos CNRS and University Pierre and Marie Curie Friday, October 23, 15

Outline and motivation Friday, October 23, 15

Outline and motivation Two well-studied problems: one from OR/TCS, the other from AI Friday, October 23, 15

Outline and motivation Two well-studied problems: one from OR/TCS, the other from AI The first problem: searching on a star (unbounded domain) Friday, October 23, 15

Outline and motivation Two well-studied problems: one from OR/TCS, the other from AI The first problem: searching on a star (unbounded domain) The second problem: how to obtain e ffj cient anytime algorithms Friday, October 23, 15

Outline and motivation Two well-studied problems: one from OR/TCS, the other from AI The first problem: searching on a star (unbounded domain) The second problem: how to obtain e ffj cient anytime algorithms Objective: address variants of these problems with a common approach Friday, October 23, 15

Outline and motivation Two well-studied problems: one from OR/TCS, the other from AI The first problem: searching on a star (unbounded domain) The second problem: how to obtain e ffj cient anytime algorithms Objective: address variants of these problems with a common approach Friday, October 23, 15

Outline and motivation Two well-studied problems: one from OR/TCS, the other from AI The first problem: searching on a star (unbounded domain) The second problem: how to obtain e ffj cient anytime algorithms Objective: address variants of these problems with a common approach Friday, October 23, 15

Outline and motivation Two well-studied problems: one from OR/TCS, the other from AI The first problem: searching on a star (unbounded domain) The second problem: how to obtain e ffj cient anytime algorithms Objective: address variants of these problems with a common approach Robots in this presentation are benign! * *certain conditions may apply Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Friday, October 23, 15

The first problem: Ray searching Performance evaluation: Competitive ratio Friday, October 23, 15

The first problem: Ray searching Performance evaluation: Competitive ratio α = sup total distance to find distance of from origin Friday, October 23, 15

The first problem: Ray searching Performance evaluation: Competitive ratio α = sup total distance to find distance of from origin Friday, October 23, 15

The second problem: Scheduling contract algorithms Friday, October 23, 15

The second problem: Scheduling contract algorithms Contract algorithms execution time given as input may return non-meaningful solutions if interrupted Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms . . . . . time Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms . . . . . time interruption at time t Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms . . . . . time interruption at time t Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms . . . . . time interruption at time t Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms . . . . . time contract execution of worst progress interruption at time t Friday, October 23, 15

The second problem: Scheduling contract algorithms Interruptible algorithms Contract algorithms execution time given as input may be interrupted at will may return non-meaningful always return meaningful solutions if interrupted solutions (improving with time) [Russell and Zilberstein 1991]: Interruptible algorithms via schedules of executions of contract algorithms . . . . . time contract execution of worst progress interruption at time t interruption time t Performance evaluation: Acceleration ratio β = sup length of t Friday, October 23, 15