1,418 research outputs found
Relaxed Schedulers Can Efficiently Parallelize Iterative Algorithms
There has been significant progress in understanding the parallelism inherent
to iterative sequential algorithms: for many classic algorithms, the depth of
the dependence structure is now well understood, and scheduling techniques have
been developed to exploit this shallow dependence structure for efficient
parallel implementations. A related, applied research strand has studied
methods by which certain iterative task-based algorithms can be efficiently
parallelized via relaxed concurrent priority schedulers. These allow for high
concurrency when inserting and removing tasks, at the cost of executing
superfluous work due to the relaxed semantics of the scheduler.
In this work, we take a step towards unifying these two research directions,
by showing that there exists a family of relaxed priority schedulers that can
efficiently and deterministically execute classic iterative algorithms such as
greedy maximal independent set (MIS) and matching. Our primary result shows
that, given a randomized scheduler with an expected relaxation factor of in
terms of the maximum allowed priority inversions on a task, and any graph on
vertices, the scheduler is able to execute greedy MIS with only an additive
factor of poly() expected additional iterations compared to an exact (but
not scalable) scheduler. This counter-intuitive result demonstrates that the
overhead of relaxation when computing MIS is not dependent on the input size or
structure of the input graph. Experimental results show that this overhead can
be clearly offset by the gain in performance due to the highly scalable
scheduler. In sum, we present an efficient method to deterministically
parallelize iterative sequential algorithms, with provable runtime guarantees
in terms of the number of executed tasks to completion.Comment: PODC 2018, pages 377-386 in proceeding
Queueing analysis of opportunistic scheduling with spatially correlated channels
International audienc
On Asymptotic Optimality of Dual Scheduling Algorithm In A Generalized Switch
Generalized switch is a model of a queueing system where parallel servers are interdependent and have time-varying service capabilities. This paper considers the dual scheduling algorithm that uses rate control and queue-length based scheduling to allocate resources for a generalized switch. We consider a saturated system in which each user has infinite amount of data to be served. We prove the asymptotic optimality of the dual scheduling algorithm for such a system, which says that the vector of average service rates of the scheduling algorithm maximizes some aggregate concave utility functions. As the fairness objectives can be achieved by appropriately choosing utility functions, the asymptotic optimality establishes the fairness properties of the dual scheduling algorithm.
The dual scheduling algorithm motivates a new architecture for scheduling, in which an additional queue is introduced to interface the user data queue and the time-varying server and to modulate the scheduling process, so as to achieve different performance objectives. Further research would include scheduling with Quality of Service guarantees with the dual scheduler, and its application and implementation in various versions of the generalized switch model
Dynamic FTSS in Asynchronous Systems: the Case of Unison
Distributed fault-tolerance can mask the effect of a limited number of
permanent faults, while self-stabilization provides forward recovery after an
arbitrary number of transient fault hit the system. FTSS protocols combine the
best of both worlds since they are simultaneously fault-tolerant and
self-stabilizing. To date, FTSS solutions either consider static (i.e. fixed
point) tasks, or assume synchronous scheduling of the system components. In
this paper, we present the first study of dynamic tasks in asynchronous
systems, considering the unison problem as a benchmark. Unison can be seen as a
local clock synchronization problem as neighbors must maintain digital clocks
at most one time unit away from each other, and increment their own clock value
infinitely often. We present many impossibility results for this difficult
problem and propose a FTSS solution when the problem is solvable that exhibits
optimal fault containment
Analysis of Probabilistic Basic Parallel Processes
Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They
are the simplest common model of concurrent programs that allows unbounded
spawning of processes. In the probabilistic version of BPPs, every process
generates other processes according to a probability distribution. We study the
decidability and complexity of fundamental qualitative problems over
probabilistic BPPs -- in particular reachability with probability 1 of
different classes of target sets (e.g. upward-closed sets). Our results concern
both the Markov-chain model, where processes are scheduled randomly, and the
MDP model, where processes are picked by a scheduler.Comment: This is the technical report for a FoSSaCS'14 pape
Weak vs. Self vs. Probabilistic Stabilization
Self-stabilization is a strong property that guarantees that a network always
resume correct behavior starting from an arbitrary initial state. Weaker
guarantees have later been introduced to cope with impossibility results:
probabilistic stabilization only gives probabilistic convergence to a correct
behavior. Also, weak stabilization only gives the possibility of convergence.
In this paper, we investigate the relative power of weak, self, and
probabilistic stabilization, with respect to the set of problems that can be
solved. We formally prove that in that sense, weak stabilization is strictly
stronger that self-stabilization. Also, we refine previous results on weak
stabilization to prove that, for practical schedule instances, a deterministic
weak-stabilizing protocol can be turned into a probabilistic self-stabilizing
one. This latter result hints at more practical use of weak-stabilization, as
such algorthms are easier to design and prove than their (probabilistic)
self-stabilizing counterparts
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