10,921 research outputs found
A Fast Constructive Algorithm For Fixed Channel Assignment Problem
With limited frequency spectrum and an increasing demand for mobile communication services, the problem of channel assignment becoems increasingly important. It has been shown that this problem is equivalent to the graph coloring problem, which is an NP-hard problem [1]. In this work, a fast constructive algorithm is introduced to solve the problem. THe objective of the algorithm is to obtain a conflict free channel assignment to cells which satisfies traffic demand requirements. THe algorithm was tested on several benchmarks problem, and conflict free results were obtained within one second. More, the quality of solution obtained was always same or better than the other reported techniques
A fast constructive algorithm for fixed channel assignment problem
With limited frequency spectrum and an increasing demand for mobile communication services, the problem of channel assignment becomes increasingly important. It has been shown that this problem is equivalent to the graph-coloring problem, which is an NP-hard problem. In this work, a fast constructive algorithm is introduced to solve the problem. The objective of the algorithm is to obtain a conflict free channel assignment to cells which satisfies traffic demand requirements. The algorithm was tested on several benchmark problems, and conflict free results were obtained a within one second. Moreover, the quality of solution obtained was always same or better than the other reported technique
Optimal Design of Multiple Description Lattice Vector Quantizers
In the design of multiple description lattice vector quantizers (MDLVQ),
index assignment plays a critical role. In addition, one also needs to choose
the Voronoi cell size of the central lattice v, the sublattice index N, and the
number of side descriptions K to minimize the expected MDLVQ distortion, given
the total entropy rate of all side descriptions Rt and description loss
probability p. In this paper we propose a linear-time MDLVQ index assignment
algorithm for any K >= 2 balanced descriptions in any dimensions, based on a
new construction of so-called K-fraction lattice. The algorithm is greedy in
nature but is proven to be asymptotically (N -> infinity) optimal for any K >=
2 balanced descriptions in any dimensions, given Rt and p. The result is
stronger when K = 2: the optimality holds for finite N as well, under some mild
conditions. For K > 2, a local adjustment algorithm is developed to augment the
greedy index assignment, and conjectured to be optimal for finite N.
Our algorithmic study also leads to better understanding of v, N and K in
optimal MDLVQ design. For K = 2 we derive, for the first time, a
non-asymptotical closed form expression of the expected distortion of optimal
MDLVQ in p, Rt, N. For K > 2, we tighten the current asymptotic formula of the
expected distortion, relating the optimal values of N and K to p and Rt more
precisely.Comment: Submitted to IEEE Trans. on Information Theory, Sep 2006 (30 pages, 7
figures
A constructive commutative quantum Lovasz Local Lemma, and beyond
The recently proven Quantum Lovasz Local Lemma generalises the well-known
Lovasz Local Lemma. It states that, if a collection of subspace constraints are
"weakly dependent", there necessarily exists a state satisfying all
constraints. It implies e.g. that certain instances of the kQSAT quantum
satisfiability problem are necessarily satisfiable, or that many-body systems
with "not too many" interactions are always frustration-free.
However, the QLLL only asserts existence; it says nothing about how to find
the state. Inspired by Moser's breakthrough classical results, we present a
constructive version of the QLLL in the setting of commuting constraints,
proving that a simple quantum algorithm converges efficiently to the required
state. In fact, we provide two different proofs, one using a novel quantum
coupling argument, the other a more explicit combinatorial analysis. Both
proofs are independent of the QLLL. So these results also provide independent,
constructive proofs of the commutative QLLL itself, but strengthen it
significantly by giving an efficient algorithm for finding the state whose
existence is asserted by the QLLL. We give an application of the constructive
commutative QLLL to convergence of CP maps.
We also extend these results to the non-commutative setting. However, our
proof of the general constructive QLLL relies on a conjecture which we are only
able to prove in special cases.Comment: 43 pages, 2 conjectures, no figures; unresolved gap in the proof; see
arXiv:1311.6474 or arXiv:1310.7766 for correct proofs of the symmetric cas
Local Multicoloring Algorithms: Computing a Nearly-Optimal TDMA Schedule in Constant Time
The described multicoloring problem has direct applications in the context of
wireless ad hoc and sensor networks. In order to coordinate the access to the
shared wireless medium, the nodes of such a network need to employ some medium
access control (MAC) protocol. Typical MAC protocols control the access to the
shared channel by time (TDMA), frequency (FDMA), or code division multiple
access (CDMA) schemes. Many channel access schemes assign a fixed set of time
slots, frequencies, or (orthogonal) codes to the nodes of a network such that
nodes that interfere with each other receive disjoint sets of time slots,
frequencies, or code sets. Finding a valid assignment of time slots,
frequencies, or codes hence directly corresponds to computing a multicoloring
of a graph . The scarcity of bandwidth, energy, and computing resources in
ad hoc and sensor networks, as well as the often highly dynamic nature of these
networks require that the multicoloring can be computed based on as little and
as local information as possible
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