scholarly journals Solving Multi-agent Path Finding on Strongly Biconnected Digraphs

2018 ◽  
Vol 62 ◽  
pp. 273-314
Author(s):  
Adi Botea ◽  
Davide Bonusi ◽  
Pavel Surynek
Keyword(s):  
Empirical Analysis ◽  
Polynomial Time ◽  
Directed Graphs ◽  
Path Finding ◽  
Undirected Graphs ◽  
Suboptimal Solutions ◽  
Polynomial Time Algorithms ◽  
Asymmetric Communication ◽  
Multi Agent

Much of the literature on suboptimal, polynomial-time algorithms for multi-agent path finding focuses on undirected graphs, where motion is permitted in both directions along a graph edge. Despite this, traveling on directed graphs is relevant in navigation domains, such as path finding in games, and asymmetric communication networks.We consider multi-agent path finding on strongly biconnected directed graphs. We show that all instances with at least two unoccupied positions have a solution, except for a particular, degenerate subclass where the graph has a cyclic shape. We present diBOX, an algorithm for multi-agent path finding on strongly biconnected directed graphs. diBOX runs in polynomial time, computes suboptimal solutions and is complete for instances on strongly biconnected digraphs with at least two unoccupied positions. We theoretically analyze properties of the algorithm and properties of strongly biconnected directed graphs that are relevant to our approach. We perform a detailed empirical analysis of diBOX, showing a good scalability. To our knowledge, our work is the first study of multi-agent path finding focused on directed graphs.

scholarly journals Solving Multi-Agent Path Finding on Strongly Biconnected Digraphs (Extended Abstract)

2018 ◽  
Author(s):  
Adi Botea ◽  
Davide Bonusi ◽  
Pavel Surynek
Keyword(s):  
Empirical Analysis ◽  
Polynomial Time ◽  
Directed Graphs ◽  
Path Finding ◽  
Suboptimal Solutions ◽  
Multi Agent

We present and evaluate diBOX, an algorithm for multi-agent path finding on strongly biconnected directed graphs. diBOX runs in polynomial time, computes suboptimal solutions and is complete for instances on strongly biconnected digraphs with at least two unoccupied positions. A detailed empirical analysis shows a good scalability for diBOX.

scholarly journals Summary: Multi-Agent Path Finding with Kinematic Constraints

2017 ◽  
Author(s):  
Wolfgang Hönig ◽  
T. K. Satish Kumar ◽  
Liron Cohen ◽  
Hang Ma ◽  
Hong Xu ◽  
...  
Keyword(s):  
Polynomial Time ◽  
Path Finding ◽  
Kinematic Constraints ◽  
Plan Execution ◽  
Differential Drive ◽  
Safety Distance ◽  
Multi Agent ◽  
And Robotics

Multi-Agent Path Finding (MAPF) is well studied in both AI and robotics. Given a discretized environment and agents with assigned start and goal locations, MAPF solvers from AI find collision-free paths for hundreds of agents with user-provided sub-optimality guarantees. However, they ignore that actual robots are subject to kinematic constraints (such as velocity limits) and suffer from imperfect plan-execution capabilities. We therefore introduce MAPF-POST to postprocess the output of a MAPF solver in polynomial time to create a plan-execution schedule that can be executed on robots. This schedule works on non-holonomic robots, considers kinematic constraints, provides a guaranteed safety distance between robots, and exploits slack to avoid time-intensive replanning in many cases. We evaluate MAPF-POST in simulation and on differential-drive robots, showcasing the practicality of our approach.

STATION PLACEMENT IN NETWORKS

2005 ◽  
Vol 15 (01n02) ◽  
pp. 117-129 ◽  
Author(s):  
CLEMENTE GALDI ◽  
CHRISTOS KAKLAMANIS ◽  
MANUELA MONTANGERO ◽  
GIUSEPPE PERSIANO
Keyword(s):  
Polynomial Time ◽  
Steiner Tree ◽  
Directed Graphs ◽  
Placement Problem ◽  
Directed Tree ◽  
Switched Networks ◽  
Polynomial Time Algorithms ◽  
Natural Variant

In this paper we study the Station Placement problem on directed graphs, a problem that has applications to efficient multicasting in circuit-switched networks. We first argue that the problem on general directed graphs can be efficiently reduced to computing bounded depth Steiner tree on complete weighted directed graphs. Then, we concentrate on the case in which the graph is a directed tree and we give polynomial time algorithms to solve the problem and a natural variant of the problem.

scholarly journals Almost Group Envy-free Allocation of Indivisible Goods and Chores

2020 ◽  
Author(s):  
Haris Aziz ◽  
Simon Rey
Keyword(s):  
Resource Allocation ◽  
Polynomial Time ◽  
Fair Allocation ◽  
Indivisible Goods ◽  
Preference Domain ◽  
Polynomial Time Algorithms ◽  
Multi Agent ◽  
Additive Utilities ◽  
Natural Classes ◽  
Allocation Of Indivisible Items

We consider a multi-agent resource allocation setting in which an agent's utility may decrease or increase when an item is allocated. We take the group envy-freeness concept that is well-established in the literature and present stronger and relaxed versions that are especially suitable for the allocation of indivisible items. Of particular interest is a concept called group envy-freeness up to one item (GEF1). We then present a clear taxonomy of the fairness concepts. We study which fairness concepts guarantee the existence of a fair allocation under which preference domain. For two natural classes of additive utilities, we design polynomial-time algorithms to compute a GEF1 allocation. We also prove that checking whether a given allocation satisfies GEF1 is coNP-complete when there are either only goods, only chores or both.

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