694 research outputs found
Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements
We consider the problem of maximizing aggregate user utilities over a
multi-hop network, subject to link capacity constraints, maximum end-to-end
delay constraints, and user throughput requirements. A user's utility is a
concave function of the achieved throughput or the experienced maximum delay.
The problem is important for supporting real-time multimedia traffic, and is
uniquely challenging due to the need of simultaneously considering maximum
delay constraints and throughput requirements. We first show that it is
NP-complete either (i) to construct a feasible solution strictly meeting all
constraints, or (ii) to obtain an optimal solution after we relax maximum delay
constraints or throughput requirements up to constant ratios. We then develop a
polynomial-time approximation algorithm named PASS. The design of PASS
leverages a novel understanding between non-convex maximum-delay-aware problems
and their convex average-delay-aware counterparts, which can be of independent
interest and suggest a new avenue for solving maximum-delay-aware network
optimization problems. Under realistic conditions, PASS achieves constant or
problem-dependent approximation ratios, at the cost of violating maximum delay
constraints or throughput requirements by up to constant or problem-dependent
ratios. PASS is practically useful since the conditions for PASS are satisfied
in many popular application scenarios. We empirically evaluate PASS using
extensive simulations of supporting video-conferencing traffic across Amazon
EC2 datacenters. Compared to existing algorithms and a conceivable baseline,
PASS obtains up to improvement of utilities, by meeting the throughput
requirements but relaxing the maximum delay constraints that are acceptable for
practical video conferencing applications
On the Min-Max-Delay Problem: NP-completeness, Algorithm, and Integrality Gap
We study a delay-sensitive information flow problem where a source streams
information to a sink over a directed graph G(V,E) at a fixed rate R possibly
using multiple paths to minimize the maximum end-to-end delay, denoted as the
Min-Max-Delay problem. Transmission over an edge incurs a constant delay within
the capacity. We prove that Min-Max-Delay is weakly NP-complete, and
demonstrate that it becomes strongly NP-complete if we require integer flow
solution. We propose an optimal pseudo-polynomial time algorithm for
Min-Max-Delay, with time complexity O(\log (Nd_{\max}) (N^5d_{\max}^{2.5})(\log
R+N^2d_{\max}\log(N^2d_{\max}))), where N = \max\{|V|,|E|\} and d_{\max} is the
maximum edge delay. Besides, we show that the integrality gap, which is defined
as the ratio of the maximum delay of an optimal integer flow to the maximum
delay of an optimal fractional flow, could be arbitrarily large
Minimizing Age-of-Information with Throughput Requirements in Multi-Path Network Communication
We consider the scenario where a sender periodically sends a batch of data to
a receiver over a multi-hop network, possibly using multiple paths. Our
objective is to minimize peak/average Age-of-Information (AoI) subject to
throughput requirements. The consideration of batch generation and multi-path
communication differentiates our AoI study from existing ones. We first show
that our AoI minimization problems are NP-hard, but only in the weak sense, as
we develop an optimal algorithm with a pseudo-polynomial time complexity. We
then prove that minimizing AoI and minimizing maximum delay are "roughly"
equivalent, in the sense that any optimal solution of the latter is an
approximate solution of the former with bounded optimality loss. We leverage
this understanding to design a general approximation framework for our
problems. It can build upon any -approximation algorithm of the maximum
delay minimization problem, to construct an -approximate solution
for minimizing AoI. Here is a constant depending on the throughput
requirements. Simulations over various network topologies validate the
effectiveness of our approach.Comment: Accepted by the ACM Twentieth International Symposium on Mobile Ad
Hoc Networking and Computing (ACM MobiHoc 2019
Sandpile Prediction on Structured Undirected Graphs
We present algorithms that compute the terminal configurations for sandpile
instances in time on trees and time on paths, where is
the number of vertices. The Abelian Sandpile model is a well-known model used
in exploring self-organized criticality. Despite a large amount of work on
other aspects of sandpiles, there have been limited results in efficiently
computing the terminal state, known as the sandpile prediction problem.
Our algorithm improves the previous best runtime of on trees
[Ramachandran-Schild SODA '17] and on paths [Moore-Nilsson '99].
To do so, we move beyond the simulation of individual events by directly
computing the number of firings for each vertex. The computation is accelerated
using splittable binary search trees. We also generalize our algorithm to adapt
at most three sink vertices, which is the first prediction algorithm faster
than mere simulation on a sandpile model with sinks.
We provide a general reduction that transforms the prediction problem on an
arbitrary graph into problems on its subgraphs separated by any vertex set .
The reduction gives a time complexity of where
denotes the total time for solving on each subgraph. In addition, we give
algorithms in time on cliques and time on pseudotrees.Comment: 66 pages, submitted to SODA2
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