871 research outputs found
Automatic frequency assignment for cellular telephones using constraint satisfaction techniques
We study the problem of automatic frequency assignment for cellular telephone
systems. The frequency assignment problem is viewed as the problem
to minimize the unsatisfied soft constraints in a constraint satisfaction problem
(CSP) over a finite domain of frequencies involving co-channel, adjacent
channel, and co-site constraints. The soft constraints are automatically derived
from signal strength prediction data. The CSP is solved using a generalized
graph coloring algorithm. Graph-theoretical results play a crucial
role in making the problem tractable. Performance results from a real-world
frequency assignment problem are presented.
We develop the generalized graph coloring algorithm by stepwise refinement,
starting from DSATUR and augmenting it with local propagation,
constraint lifting, intelligent backtracking, redundancy avoidance, and iterative
deepening
Solving Hard Computational Problems Efficiently: Asymptotic Parametric Complexity 3-Coloring Algorithm
Many practical problems in almost all scientific and technological
disciplines have been classified as computationally hard (NP-hard or even
NP-complete). In life sciences, combinatorial optimization problems frequently
arise in molecular biology, e.g., genome sequencing; global alignment of
multiple genomes; identifying siblings or discovery of dysregulated pathways.In
almost all of these problems, there is the need for proving a hypothesis about
certain property of an object that can be present only when it adopts some
particular admissible structure (an NP-certificate) or be absent (no admissible
structure), however, none of the standard approaches can discard the hypothesis
when no solution can be found, since none can provide a proof that there is no
admissible structure. This article presents an algorithm that introduces a
novel type of solution method to "efficiently" solve the graph 3-coloring
problem; an NP-complete problem. The proposed method provides certificates
(proofs) in both cases: present or absent, so it is possible to accept or
reject the hypothesis on the basis of a rigorous proof. It provides exact
solutions and is polynomial-time (i.e., efficient) however parametric. The only
requirement is sufficient computational power, which is controlled by the
parameter . Nevertheless, here it is proved that the
probability of requiring a value of to obtain a solution for a
random graph decreases exponentially: , making
tractable almost all problem instances. Thorough experimental analyses were
performed. The algorithm was tested on random graphs, planar graphs and
4-regular planar graphs. The obtained experimental results are in accordance
with the theoretical expected results.Comment: Working pape
The backtracking survey propagation algorithm for solving random K-SAT problems
Discrete combinatorial optimization has a central role in many scientific
disciplines, however, for hard problems we lack linear time algorithms that
would allow us to solve very large instances. Moreover, it is still unclear
what are the key features that make a discrete combinatorial optimization
problem hard to solve. Here we study random K-satisfiability problems with
, which are known to be very hard close to the SAT-UNSAT threshold,
where problems stop having solutions. We show that the backtracking survey
propagation algorithm, in a time practically linear in the problem size, is
able to find solutions very close to the threshold, in a region unreachable by
any other algorithm. All solutions found have no frozen variables, thus
supporting the conjecture that only unfrozen solutions can be found in linear
time, and that a problem becomes impossible to solve in linear time when all
solutions contain frozen variables.Comment: 11 pages, 10 figures. v2: data largely improved and manuscript
rewritte
A High-Performance Triple Patterning Layout Decomposer with Balanced Density
Triple patterning lithography (TPL) has received more and more attentions
from industry as one of the leading candidate for 14nm/11nm nodes. In this
paper, we propose a high performance layout decomposer for TPL. Density
balancing is seamlessly integrated into all key steps in our TPL layout
decomposition, including density-balanced semi-definite programming (SDP),
density-based mapping, and density-balanced graph simplification. Our new TPL
decomposer can obtain high performance even compared to previous
state-of-the-art layout decomposers which are not balanced-density aware, e.g.,
by Yu et al. (ICCAD'11), Fang et al. (DAC'12), and Kuang et al. (DAC'13).
Furthermore, the balanced-density version of our decomposer can provide more
balanced density which leads to less edge placement error (EPE), while the
conflict and stitch numbers are still very comparable to our
non-balanced-density baseline
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
Breaking Instance-Independent Symmetries In Exact Graph Coloring
Code optimization and high level synthesis can be posed as constraint
satisfaction and optimization problems, such as graph coloring used in register
allocation. Graph coloring is also used to model more traditional CSPs relevant
to AI, such as planning, time-tabling and scheduling. Provably optimal
solutions may be desirable for commercial and defense applications.
Additionally, for applications such as register allocation and code
optimization, naturally-occurring instances of graph coloring are often small
and can be solved optimally. A recent wave of improvements in algorithms for
Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests
generic problem-reduction methods, rather than problem-specific heuristics,
because (1) heuristics may be upset by new constraints, (2) heuristics tend to
ignore structure, and (3) many relevant problems are provably inapproximable.
Problem reductions often lead to highly symmetric SAT instances, and
symmetries are known to slow down SAT solvers. In this work, we compare several
avenues for symmetry breaking, in particular when certain kinds of symmetry are
present in all generated instances. Our focus on reducing CSPs to SAT allows us
to leverage recent dramatic improvement in SAT solvers and automatically
benefit from future progress. We can use a variety of black-box SAT solvers
without modifying their source code because our symmetry-breaking techniques
are static, i.e., we detect symmetries and add symmetry breaking predicates
(SBPs) during pre-processing.
An important result of our work is that among the types of
instance-independent SBPs we studied and their combinations, the simplest and
least complete constructions are the most effective. Our experiments also
clearly indicate that instance-independent symmetries should mostly be
processed together with instance-specific symmetries rather than at the
specification level, contrary to what has been suggested in the literature
Knowledge-based design of generate-and-patch problem solvers that solve global resource assignment problems
We present MENDER, a knowledge based system that implements software design techniques that are specialized to automatically compile generate-and-patch problem solvers that satisfy global resource assignments problems. We provide empirical evidence of the superior performance of generate-and-patch over generate-and-test: even with constrained generation, for a global constraint in the domain of '2D-floorplanning'. For a second constraint in '2D-floorplanning' we show that even when it is possible to incorporate the constraint into a constrained generator, a generate-and-patch problem solver may satisfy the constraint more rapidly. We also briefly summarize how an extended version of our system applies to a constraint in the domain of 'multiprocessor scheduling'
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