76,441 research outputs found
A Competitive Analysis of Online Multi-Agent Path Finding
We study online Multi-Agent Path Finding (MAPF), where new agents are
constantly revealed over time and all agents must find collision-free paths to
their given goal locations. We generalize existing complexity results of
(offline) MAPF to online MAPF. We classify online MAPF algorithms into
different categories based on (1) controllability (the set of agents that they
can plan paths for at each time) and (2) rationality (the quality of paths they
plan) and study the relationships between them. We perform a competitive
analysis for each category of online MAPF algorithms with respect to
commonly-used objective functions. We show that a naive algorithm that routes
newly-revealed agents one at a time in sequence achieves a competitive ratio
that is asymptotically bounded from both below and above by the number of
agents with respect to flowtime and makespan. We then show a counter-intuitive
result that, if rerouting of previously-revealed agents is not allowed, any
rational online MAPF algorithms, including ones that plan optimal paths for all
newly-revealed agents, have the same asymptotic competitive ratio as the naive
algorithm, even on 2D 4-neighbor grids. We also derive constant lower bounds on
the competitive ratio of any rational online MAPF algorithms that allow
rerouting. The results thus provide theoretical insights into the effectiveness
of using MAPF algorithms in an online setting for the first time.Comment: Published at ICAPS 202
Dynamic online resource allocation problems
Online resource allocation problems consider assigning a limited number of available resources to sequentially arriving requests with the objective to maximize rewards. With the emergence of e-business, applications such as online order fulfillment and customer service require real-time resource allocation decisions to guarantee high service quality and customer satisfaction. Other typical applications include operation room scheduling, organ transplant, and passenger screening in aviation security. This dissertation approaches the dynamic online resource allocation problem by considering two models: multi-objective sequential stochastic assignment problems and online interval scheduling problems.
Multi-objective sequential stochastic assignment problems are a class of matching problems. A fixed number of jobs arrive sequentially to be assigned to one of the available workers, with an n-dimensional value vector revealed upon each arrival. The objective is to maximize the reward vector given by the product of the job value vector and worker's success rate. We conduct a complete asymptotic analysis for three classes of Pareto optimal policies, with convergence rates and asymptotic objective values provided.
Online interval scheduling problems consider reusable resources, where an adversarial sequence of jobs with fixed lengths are to be assigned on available machines. The objective is to maximize the total reward for completed jobs given by the product of the job value and the machine weight. For homogeneous machines, we propose a Pairing-m algorithm, which is 2-competitive for even m and (2+2/m)-competitive for odd m. For heterogeneous machines, two classes of approximation algorithms, Cooperative Greedy algorithms and Prioritized Greedy algorithms, are compared using competitive ratios with respect to varying machine weight ratios. We also provide lower bounds for competitive ratios of deterministic online scheduling algorithms in various scenarios.
Stochastic online interval scheduling problems consider a sequence of jobs drawn from a given distribution. For identically and independently distributed jobs with a known distribution, we propose 2-competitive online algorithms for both equal-length and memoryless-length jobs. For job sequences with a random order of arrivals, we propose e-competitive and e^2/(e-1)-competitive online algorithms for both equal-length and memoryless-length jobs. We further extend these results to jobs with a random order of arrivals and geometric arrivals with parameter p.
We propose a primal-dual analysis framework for online interval scheduling algorithms for both adversarial and stochastic job sequences. We formulate the online interval scheduling as a linear program with a corresponding dual program. For stochastic job sequences, we use complementary slackness conditions and weak duality to derive optimal algorithms and upper bounds for the optimal reward, respectively. For adversarial sequences, we use weak duality to compute the competitive ratios of scheduling algorithms
SELFISHMIGRATE: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors
We consider the classical problem of minimizing the total weighted flow-time
for unrelated machines in the online \emph{non-clairvoyant} setting. In this
problem, a set of jobs arrive over time to be scheduled on a set of
machines. Each job has processing length , weight , and is
processed at a rate of when scheduled on machine . The online
scheduler knows the values of and upon arrival of the job,
but is not aware of the quantity . We present the {\em first} online
algorithm that is {\em scalable} ((1+\eps)-speed
-competitive for any constant \eps > 0) for the
total weighted flow-time objective. No non-trivial results were known for this
setting, except for the most basic case of identical machines. Our result
resolves a major open problem in online scheduling theory. Moreover, we also
show that no job needs more than a logarithmic number of migrations. We further
extend our result and give a scalable algorithm for the objective of minimizing
total weighted flow-time plus energy cost for the case of unrelated machines
and obtain a scalable algorithm. The key algorithmic idea is to let jobs
migrate selfishly until they converge to an equilibrium. Towards this end, we
define a game where each job's utility which is closely tied to the
instantaneous increase in the objective the job is responsible for, and each
machine declares a policy that assigns priorities to jobs based on when they
migrate to it, and the execution speeds. This has a spirit similar to
coordination mechanisms that attempt to achieve near optimum welfare in the
presence of selfish agents (jobs). To the best our knowledge, this is the first
work that demonstrates the usefulness of ideas from coordination mechanisms and
Nash equilibria for designing and analyzing online algorithms
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