869 research outputs found
Flow Rounding
We consider flow rounding: finding an integral flow from a fractional flow.
Costed flow rounding asks that we find an integral flow with no worse cost.
Randomized flow rounding requires we randomly find an integral flow such that
the expected flow along each edge matches the fractional flow. Both problems
are reduced to cycle canceling, for which we develop an
algorithm.Comment: 10 pages, 3 figure
Delay Minimizing User Association in Cellular Networks via Hierarchically Well-Separated Trees
We study downlink delay minimization within the context of cellular user
association policies that map mobile users to base stations. We note the delay
minimum user association problem fits within a broader class of network utility
maximization and can be posed as a non-convex quadratic program. This
non-convexity motivates a split quadratic objective function that captures the
original problem's inherent tradeoff: association with a station that provides
the highest signal-to-interference-plus-noise ratio (SINR) vs. a station that
is least congested. We find the split-term formulation is amenable to
linearization by embedding the base stations in a hierarchically well-separated
tree (HST), which offers a linear approximation with constant distortion. We
provide a numerical comparison of several problem formulations and find that
with appropriate optimization parameter selection, the quadratic reformulation
produces association policies with sum delays that are close to that of the
original network utility maximization. We also comment on the more difficult
problem when idle base stations (those without associated users) are
deactivated.Comment: 6 pages, 5 figures. Submitted on 2013-10-03 to the 2015 IEEE
International Conference on Communications (ICC). Accepted on 2015-01-09 to
the 2015 IEEE International Conference on Communications (ICC
Approximate and Incremental Network Function Placement
The virtualization and softwarization of modern computer networks introduces
interesting new opportunities for a more flexible placement of network
functions and middleboxes (firewalls, proxies, traffic optimizers, virtual
switches, etc.). This paper studies approximation algorithms for the
incremental deployment of a minimum number of middleboxes at optimal locations,
such that capacity constraints at the middleboxes and length constraints on the
communication routes are respected. Our main contribution is a new, purely
combinatorial and rigorous proof for the submodularity of the function
maximizing the number of communication requests that can be served by a given
set of middleboxes. Our proof allows us to devise a deterministic approximation
algorithm which uses an augmenting path approach to compute the submodular
function. This algorithm does not require any changes to the locations of
existing middleboxes or the preemption of previously served communication pairs
when additional middleboxes are deployed, previously accepted communication
pairs just can be handed over to another middlebox. It is hence particularly
attractive for incremental deployments.We prove that the achieved
polynomial-time approximation bound is optimal, unless P = NP. This paper also
initiates the study of a weighted problem variant, in which entire groups of
nodes need to communicate via a middlebox (e.g., a multiplexer or a shared
object), possibly at different rates. We present an LP relaxation and
randomized rounding algorithm for this problem, leveraging an interesting
connection to scheduling
Competitive Algorithms from Competitive Equilibria: Non-Clairvoyant Scheduling under Polyhedral Constraints
We introduce and study a general scheduling problem that we term the Packing
Scheduling problem. In this problem, jobs can have different arrival times and
sizes; a scheduler can process job at rate , subject to arbitrary
packing constraints over the set of rates () of the outstanding jobs.
The PSP framework captures a variety of scheduling problems, including the
classical problems of unrelated machines scheduling, broadcast scheduling, and
scheduling jobs of different parallelizability. It also captures scheduling
constraints arising in diverse modern environments ranging from individual
computer architectures to data centers. More concretely, PSP models
multidimensional resource requirements and parallelizability, as well as
network bandwidth requirements found in data center scheduling.
In this paper, we design non-clairvoyant online algorithms for PSP and its
special cases -- in this setting, the scheduler is unaware of the sizes of
jobs. Our two main results are, 1) a constant competitive algorithm for
minimizing total weighted completion time for PSP and 2)a scalable algorithm
for minimizing the total flow-time on unrelated machines, which is a special
case of PSP.Comment: Accepted for publication in STOC 201
Routing of Electric Vehicles: Constrained Shortest Path Problems with Resource Recovering Nodes
We consider a constrained shortest path problem with the possibility to refill the resource at certain nodes. This problem is motivated by routing electric vehicles with a comparatively short cruising range due to the limited battery capacity. Thus, for longer distances the battery has to be recharged on the way. Furthermore, electric vehicles can recuperate energy during downhill drive. We extend the common constrained shortest path problem to arbitrary costs on edges and we allow regaining resources at the cost of higher travel time. We show that this yields not shortest paths but shortest walks that may contain an arbitrary number of cycles. We study the structure of optimal solutions and develop approximation algorithms for finding short walks under mild assumptions on charging functions. We also address a corresponding network flow problem that generalizes these walks
Energy Efficient Scheduling and Routing via Randomized Rounding
We propose a unifying framework based on configuration linear programs and
randomized rounding, for different energy optimization problems in the dynamic
speed-scaling setting. We apply our framework to various scheduling and routing
problems in heterogeneous computing and networking environments. We first
consider the energy minimization problem of scheduling a set of jobs on a set
of parallel speed scalable processors in a fully heterogeneous setting. For
both the preemptive-non-migratory and the preemptive-migratory variants, our
approach allows us to obtain solutions of almost the same quality as for the
homogeneous environment. By exploiting the result for the
preemptive-non-migratory variant, we are able to improve the best known
approximation ratio for the single processor non-preemptive problem.
Furthermore, we show that our approach allows to obtain a constant-factor
approximation algorithm for the power-aware preemptive job shop scheduling
problem. Finally, we consider the min-power routing problem where we are given
a network modeled by an undirected graph and a set of uniform demands that have
to be routed on integral routes from their sources to their destinations so
that the energy consumption is minimized. We improve the best known
approximation ratio for this problem.Comment: 27 page
Pricing Mortgages: An Interpretation of the Models and Results
Mortgages, like all debt securities, can be viewed as risk-free assets plus or minus contingent claims that can be usefully viewed as options. The most important options are: prepayment, which is a call option giving the borrower the right to buy back the mortgage at par, and default, which is a put option giving the borrower the right to sell the house in exchange for the mortgage. This paper reviews and interprets the large and growing body of literature that applies recent results of option pricing models to mortgages. We also provide a critique of the models and suggest directions for future research.
Source Routing and Scheduling in Packet Networks
We study {\em routing} and {\em scheduling} in packet-switched networks. We
assume an adversary that controls the injection time, source, and destination
for each packet injected. A set of paths for these packets is {\em admissible}
if no link in the network is overloaded. We present the first on-line routing
algorithm that finds a set of admissible paths whenever this is feasible. Our
algorithm calculates a path for each packet as soon as it is injected at its
source using a simple shortest path computation. The length of a link reflects
its current congestion. We also show how our algorithm can be implemented under
today's Internet routing paradigms.
When the paths are known (either given by the adversary or computed as above)
our goal is to schedule the packets along the given paths so that the packets
experience small end-to-end delays. The best previous delay bounds for
deterministic and distributed scheduling protocols were exponential in the path
length. In this paper we present the first deterministic and distributed
scheduling protocol that guarantees a polynomial end-to-end delay for every
packet.
Finally, we discuss the effects of combining routing with scheduling. We
first show that some unstable scheduling protocols remain unstable no matter
how the paths are chosen. However, the freedom to choose paths can make a
difference. For example, we show that a ring with parallel links is stable for
all greedy scheduling protocols if paths are chosen intelligently, whereas this
is not the case if the adversary specifies the paths.Comment: A preliminary version of this paper appeared in the Proceedings of
the 42th IEEE Annual Symposium on Foundations of Computer Science, FOCS 200
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