64 research outputs found
Minimizing Flow-Time on Unrelated Machines
We consider some flow-time minimization problems in the unrelated machines
setting. In this setting, there is a set of machines and a set of jobs,
and each job has a machine dependent processing time of on machine
. The flow-time of a job is the total time the job spends in the system
(completion time minus its arrival time), and is one of the most natural
quality of service measure. We show the following two results: an
approximation algorithm for minimizing the
total-flow time, and an approximation for minimizing the maximum
flow-time. Here is the ratio of maximum to minimum job size. These are the
first known poly-logarithmic guarantees for both the problems.Comment: The new version fixes some typos in the previous version. The paper
is accepted for publication in STOC 201
Constant-Competitive Prior-Free Auction with Ordered Bidders
A central problem in Microeconomics is to design auctions with good revenue
properties. In this setting, the bidders' valuations for the items are private
knowledge, but they are drawn from publicly known prior distributions. The goal
is to find a truthful auction (no bidder can gain in utility by misreporting
her valuation) that maximizes the expected revenue.
Naturally, the optimal-auction is sensitive to the prior distributions. An
intriguing question is to design a truthful auction that is oblivious to these
priors, and yet manages to get a constant factor of the optimal revenue. Such
auctions are called prior-free.
Goldberg et al. presented a constant-approximate prior-free auction when
there are identical copies of an item available in unlimited supply, bidders
are unit-demand, and their valuations are drawn from i.i.d. distributions. The
recent work of Leonardi et al. [STOC 2012] generalized this problem to non
i.i.d. bidders, assuming that the auctioneer knows the ordering of their
reserve prices. Leonardi et al. proposed a prior-free auction that achieves a
approximation. We improve upon this result, by giving the first
prior-free auction with constant approximation guarantee.Comment: The same result has been obtained independently by E. Koutsoupias, S.
Leonardi and T. Roughgarde
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
An improved algorithm for incremental cycle detection and topological ordering in sparse graphs
We consider the problem of incremental cycle detection and topological ordering in a directed graph G = (V, E) with |V| = n nodes. In this setting, initially the edge-set E of the graph is empty. Subsequently, at each time-step an edge gets inserted into G. After every edge-insertion, we have to report if the current graph contains a cycle, and as long as the graph remains acyclic, we have to maintain a topological ordering of the node-set V. Let m be the total number of edges that get inserted into G. We present a randomized algorithm for this problem with Õ(m4/3) total expected update time.
Our result improves the Õ(m • min(m1/2, n2/3)) total update time bound of [5, 9, 10, 7]. In particular, for m = O(n), our result breaks the longstanding barrier on the total update time. Furthermore, whenever m = o(n3/2), our result improves upon the recently obtained total update time bound of [6]. We note that if m = Ω(n3/2), then the algorithm of [5, 4, 7], which has Õ(n2) total update time, beats the performance of the time algorithm of [6]. It follows that we improve upon the total update time of the algorithm of [6] in the “interesting” range of sparsity where m = o(n3/2).
Our result also happens to be the first one that breaks the lower bound of [9] on the total update time of any local algorithm for a nontrivial range of sparsity. Specifically, the total update time of our algorithm is whenever . From a technical perspective, we obtain our result by combining the algorithm of [6] with the balanced search framework of [10]
Truth and Regret in Online Scheduling
We consider a scheduling problem where a cloud service provider has multiple
units of a resource available over time. Selfish clients submit jobs, each with
an arrival time, deadline, length, and value. The service provider's goal is to
implement a truthful online mechanism for scheduling jobs so as to maximize the
social welfare of the schedule. Recent work shows that under a stochastic
assumption on job arrivals, there is a single-parameter family of mechanisms
that achieves near-optimal social welfare. We show that given any such family
of near-optimal online mechanisms, there exists an online mechanism that in the
worst case performs nearly as well as the best of the given mechanisms. Our
mechanism is truthful whenever the mechanisms in the given family are truthful
and prompt, and achieves optimal (within constant factors) regret.
We model the problem of competing against a family of online scheduling
mechanisms as one of learning from expert advice. A primary challenge is that
any scheduling decisions we make affect not only the payoff at the current
step, but also the resource availability and payoffs in future steps.
Furthermore, switching from one algorithm (a.k.a. expert) to another in an
online fashion is challenging both because it requires synchronization with the
state of the latter algorithm as well as because it affects the incentive
structure of the algorithms. We further show how to adapt our algorithm to a
non-clairvoyant setting where job lengths are unknown until jobs are run to
completion. Once again, in this setting, we obtain truthfulness along with
asymptotically optimal regret (within poly-logarithmic factors)
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