27,515 research outputs found
Cross-layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks
This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc
wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints.
By dual decomposition, the resource allocation problem
naturally decomposes into three subproblems: congestion control,
routing and scheduling that interact through congestion price.
The global convergence property of this algorithm is proved. We
next extend the dual algorithm to handle networks with timevarying
channels and adaptive multi-rate devices. The stability
of the resulting system is established, and its performance is
characterized with respect to an ideal reference system which
has the best feasible rate region at link layer.
We then generalize the aforementioned results to a general
model of queueing network served by a set of interdependent
parallel servers with time-varying service capabilities, which
models many design problems in communication networks. We
show that for a general convex optimization problem where a
subset of variables lie in a polytope and the rest in a convex set,
the dual-based algorithm remains stable and optimal when the
constraint set is modulated by an irreducible finite-state Markov
chain. This paper thus presents a step toward a systematic way
to carry out cross-layer design in the framework of “layering as
optimization decomposition” for time-varying channel models
Setting Parameters by Example
We introduce a class of "inverse parametric optimization" problems, in which
one is given both a parametric optimization problem and a desired optimal
solution; the task is to determine parameter values that lead to the given
solution. We describe algorithms for solving such problems for minimum spanning
trees, shortest paths, and other "optimal subgraph" problems, and discuss
applications in multicast routing, vehicle path planning, resource allocation,
and board game programming.Comment: 13 pages, 3 figures. To be presented at 40th IEEE Symp. Foundations
of Computer Science (FOCS '99
Reducing Electricity Demand Charge for Data Centers with Partial Execution
Data centers consume a large amount of energy and incur substantial
electricity cost. In this paper, we study the familiar problem of reducing data
center energy cost with two new perspectives. First, we find, through an
empirical study of contracts from electric utilities powering Google data
centers, that demand charge per kW for the maximum power used is a major
component of the total cost. Second, many services such as Web search tolerate
partial execution of the requests because the response quality is a concave
function of processing time. Data from Microsoft Bing search engine confirms
this observation.
We propose a simple idea of using partial execution to reduce the peak power
demand and energy cost of data centers. We systematically study the problem of
scheduling partial execution with stringent SLAs on response quality. For a
single data center, we derive an optimal algorithm to solve the workload
scheduling problem. In the case of multiple geo-distributed data centers, the
demand of each data center is controlled by the request routing algorithm,
which makes the problem much more involved. We decouple the two aspects, and
develop a distributed optimization algorithm to solve the large-scale request
routing problem. Trace-driven simulations show that partial execution reduces
cost by for one data center, and by for geo-distributed
data centers together with request routing.Comment: 12 page
Fast Detour Computation for Ride Sharing
Todays ride sharing services still mimic a better billboard. They list the
offers and allow to search for the source and target city, sometimes enriched
with radial search. So finding a connection between big cities is quite easy.
These places are on a list of designated origin and distination points. But
when you want to go from a small town to another small town, even when they are
next to a freeway, you run into problems. You can't find offers that would or
could pass by the town easily with little or no detour. We solve this
interesting problem by presenting a fast algorithm that computes the offers
with the smallest detours w.r.t. a request. Our experiments show that the
problem is efficiently solvable in times suitable for a web service
implementation. For realistic database size we achieve lookup times of about
5ms and a matching rate of 90% instead of just 70% for the simple matching
algorithms used today.Comment: 5 pages, 2 figure environment, 4 includegraphic
Models and Algorithms for Some Covering Problems on Graphs
2014 - 2015Several real-life problems as well as problems of theoretical importance
within the field of Operations Research are combinatorial in nature.
Combinatorial Optimization deals with decision-making problems defined
on a discrete space. Out of a finite or countably infinite set of
feasible solutions, one has to choose the best one according to an objective
function. Many of these problems can be modeled on undirected
or directed graphs. Some of the most important problems studied in
this area include the Minimum Spanning Tree Problem, the Traveling
Salesman Problem, the Vehicle Routing Problem, the Matching Problem,
the Maximum Flow Problem. Some combinatorial optimization problems
have been modeled on colored (labeled) graphs. The colors can be
associated to the vertices as well as to the edges of the graph, depending
on the problem. The Minimum Labeling Spanning Tree Problem and
the Minimum Labeling Hamiltonian Cycle Problem are two examples
of problems defined on edge-colored graphs.
Combinatorial optimization problems can be divided into two groups,
according to their complexity. The problems that are easy to solve, i.e.
problems polynomially solvable, and those that are hard, i.e. for which
no polynomial time algorithm exists. Many of the well-known combinatorial
optimization problems defined on graphs are hard problems in
general. However, if we know more about the structure of the graph,
the problems can become more tractable. In some cases, they can even
be shown to be polynomial-time solvable. This particularly holds for
trees...[edited by Author]XIV n.s
The edge-disjoint path problem on random graphs by message-passing
We present a message-passing algorithm to solve the edge disjoint path
problem (EDP) on graphs incorporating under a unique framework both traffic
optimization and path length minimization. The min-sum equations for this
problem present an exponential computational cost in the number of paths. To
overcome this obstacle we propose an efficient implementation by mapping the
equations onto a weighted combinatorial matching problem over an auxiliary
graph. We perform extensive numerical simulations on random graphs of various
types to test the performance both in terms of path length minimization and
maximization of the number of accommodated paths. In addition, we test the
performance on benchmark instances on various graphs by comparison with
state-of-the-art algorithms and results found in the literature. Our
message-passing algorithm always outperforms the others in terms of the number
of accommodated paths when considering non trivial instances (otherwise it
gives the same trivial results). Remarkably, the largest improvement in
performance with respect to the other methods employed is found in the case of
benchmarks with meshes, where the validity hypothesis behind message-passing is
expected to worsen. In these cases, even though the exact message-passing
equations do not converge, by introducing a reinforcement parameter to force
convergence towards a sub optimal solution, we were able to always outperform
the other algorithms with a peak of 27% performance improvement in terms of
accommodated paths. On random graphs, we numerically observe two separated
regimes: one in which all paths can be accommodated and one in which this is
not possible. We also investigate the behaviour of both the number of paths to
be accommodated and their minimum total length.Comment: 14 pages, 8 figure
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