53 research outputs found
From coordinate subspaces over finite fields to ideal multipartite uniform clutters
Take a prime power , an integer , and a coordinate subspace
over the Galois field . One can associate with
an -partite -uniform clutter , where every part has size
and there is a bijection between the vectors in and the members of
.
In this paper, we determine when the clutter is ideal, a
property developed in connection to Packing and Covering problems in the areas
of Integer Programming and Combinatorial Optimization. Interestingly, the
characterization differs depending on whether is , a higher power of
, or otherwise. Each characterization uses crucially that idealness is a
minor-closed property: first the list of excluded minors is identified, and
only then is the global structure determined. A key insight is that idealness
of depends solely on the underlying matroid of .
Our theorems also extend from idealness to the stronger max-flow min-cut
property. As a consequence, we prove the Replication and Conjectures
for this class of clutters.Comment: 32 pages, 6 figure
Dyadic linear programming and extensions
A rational number is dyadic if it has a finite binary representation ,
where is an integer and is a nonnegative integer. Dyadic rationals are
important for numerical computations because they have an exact representation
in floating-point arithmetic on a computer. A vector is dyadic if all its
entries are dyadic rationals. We study the problem of finding a dyadic optimal
solution to a linear program, if one exists. We show how to solve dyadic linear
programs in polynomial time. We give bounds on the size of the support of a
solution as well as on the size of the denominators. We identify properties
that make the solution of dyadic linear programs possible: closure under
addition and negation, and density, and we extend the algorithmic framework
beyond the dyadic case
The Edmonds-Giles Conjecture and its Relaxations
Given a directed graph, a directed cut is a cut with all arcs oriented in the same direction, and a directed join is a set of arcs which intersects every directed cut at least once. Edmonds and Giles conjectured for all weighted directed graphs, the minimum weight of a directed cut is equal to the maximum size of a packing of directed joins. Unfortunately, the conjecture is false; a counterexample was first given by Schrijver. However its âdualâ statement, that the minimum weight of a dijoin is equal to the maximum number of dicuts in a packing, was shown to be true by Luchessi and Younger.
Various relaxations of the conjecture have been considered; Woodallâs conjecture remains open, which asks the same question for unweighted directed graphs, and Edmond- Giles conjecture was shown to be true in the special case of source-sink connected directed graphs. Following these inquries, this thesis explores different relaxations of the Edmond- Giles conjecture
On packing dijoins in digraphs and weighted digraphs
In this paper, we make some progress in addressing Woodall's Conjecture, and
the refuted Edmonds-Giles Conjecture on packing dijoins in unweighted and
weighted digraphs. Let be a digraph, and let . Suppose every dicut has weight at least , for some integer . Let , where each is
the integer in equal to
mod . In this paper, we prove the following results, amongst others: (1)
If , then can be partitioned into a dijoin and a
-dijoin. (2) If , then there is an
equitable -weighted packing of dijoins of size . (3) If
, then there is a -weighted packing of dijoins of size
. (4) If , , and , then can be
partitioned into three dijoins.
Each result is best possible: (1) and (4) do not hold for general , (2)
does not hold for even if , and (3) does not hold
for . The results are rendered possible by a \emph{Decompose,
Lift, and Reduce procedure}, which turns into a set of
\emph{sink-regular weighted -bipartite digraphs}, each of which
is a weighted digraph where every vertex is a sink of weighted degree or
a source of weighted degree , and every dicut has weight at least
. Our results give rise to a number of approaches for resolving Woodall's
Conjecture, fixing the refuted Edmonds-Giles Conjecture, and the
Conjecture for the clutter of minimal dijoins. They also show an intriguing
connection to Barnette's Conjecture.Comment: 71 page
Cooperative Radio Communications for Green Smart Environments
The demand for mobile connectivity is continuously increasing, and by 2020 Mobile and Wireless Communications will serve not only very dense populations of mobile phones and nomadic computers, but also the expected multiplicity of devices and sensors located in machines, vehicles, health systems and city infrastructures. Future Mobile Networks are then faced with many new scenarios and use cases, which will load the networks with different data traffic patterns, in new or shared spectrum bands, creating new specific requirements. This book addresses both the techniques to model, analyse and optimise the radio links and transmission systems in such scenarios, together with the most advanced radio access, resource management and mobile networking technologies. This text summarises the work performed by more than 500 researchers from more than 120 institutions in Europe, America and Asia, from both academia and industries, within the framework of the COST IC1004 Action on "Cooperative Radio Communications for Green and Smart Environments". The book will have appeal to graduates and researchers in the Radio Communications area, and also to engineers working in the Wireless industry. Topics discussed in this book include: ⢠Radio waves propagation phenomena in diverse urban, indoor, vehicular and body environments⢠Measurements, characterization, and modelling of radio channels beyond 4G networks⢠Key issues in Vehicle (V2X) communication⢠Wireless Body Area Networks, including specific Radio Channel Models for WBANs⢠Energy efficiency and resource management enhancements in Radio Access Networks⢠Definitions and models for the virtualised and cloud RAN architectures⢠Advances on feasible indoor localization and tracking techniques⢠Recent findings and innovations in antenna systems for communications⢠Physical Layer Network Coding for next generation wireless systems⢠Methods and techniques for MIMO Over the Air (OTA) testin
Clean clutters and dyadic fractional packings
A vector is dyadic if each of its entries is a dyadic rational number, i.e., an integer multiple of 1 2k for some nonnegative integer k. We prove that every clean clutter with a covering number of at least two has a dyadic fractional packing of value two. This result is best possible for there exist clean clutters with a covering number of three and no dyadic fractional packing of value three. Examples of clean clutters include ideal clutters, binary clutters, and clutters without an intersecting minor. Our proof is constructive and leads naturally to an albeit exponential algorithm. We improve the running time to quasi-polynomial in the rank of the input, and to polynomial in the binary cas
Modelling, Simulation and Data Analysis in Acoustical Problems
Modelling and simulation in acoustics is currently gaining importance. In fact, with the development and improvement of innovative computational techniques and with the growing need for predictive models, an impressive boost has been observed in several research and application areas, such as noise control, indoor acoustics, and industrial applications. This led us to the proposal of a special issue about âModelling, Simulation and Data Analysis in Acoustical Problemsâ, as we believe in the importance of these topics in modern acousticsâ studies. In total, 81 papers were submitted and 33 of them were published, with an acceptance rate of 37.5%. According to the number of papers submitted, it can be affirmed that this is a trending topic in the scientific and academic community and this special issue will try to provide a future reference for the research that will be developed in coming years
Sensor Signal and Information Processing II
In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing
- âŚ