3,122 research outputs found
On Backtracking in Real-time Heuristic Search
Real-time heuristic search algorithms are suitable for situated agents that
need to make their decisions in constant time. Since the original work by Korf
nearly two decades ago, numerous extensions have been suggested. One of the
most intriguing extensions is the idea of backtracking wherein the agent
decides to return to a previously visited state as opposed to moving forward
greedily. This idea has been empirically shown to have a significant impact on
various performance measures. The studies have been carried out in particular
empirical testbeds with specific real-time search algorithms that use
backtracking. Consequently, the extent to which the trends observed are
characteristic of backtracking in general is unclear. In this paper, we present
the first entirely theoretical study of backtracking in real-time heuristic
search. In particular, we present upper bounds on the solution cost exponential
and linear in a parameter regulating the amount of backtracking. The results
hold for a wide class of real-time heuristic search algorithms that includes
many existing algorithms as a small subclass
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
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Data Structures and Algorithms for Disjoint Set Union Problems
This paper surveys algorithmic techniques and data structures that have been proposed to solve the set union problem and its variants. Their discovery required a new set of algorithmic tools that have proven useful in other areas. Special attention is devoted to recent extensions of the original set union problem, and some effort is made to provide a unifying theoretical framework for this growing body of algorithms
On Neighborhood Tree Search
We consider the neighborhood tree induced by alternating the use of different
neighborhood structures within a local search descent. We investigate the issue
of designing a search strategy operating at the neighborhood tree level by
exploring different paths of the tree in a heuristic way. We show that allowing
the search to 'backtrack' to a previously visited solution and resuming the
iterative variable neighborhood descent by 'pruning' the already explored
neighborhood branches leads to the design of effective and efficient search
heuristics. We describe this idea by discussing its basic design components
within a generic algorithmic scheme and we propose some simple and intuitive
strategies to guide the search when traversing the neighborhood tree. We
conduct a thorough experimental analysis of this approach by considering two
different problem domains, namely, the Total Weighted Tardiness Problem
(SMTWTP), and the more sophisticated Location Routing Problem (LRP). We show
that independently of the considered domain, the approach is highly
competitive. In particular, we show that using different branching and
backtracking strategies when exploring the neighborhood tree allows us to
achieve different trade-offs in terms of solution quality and computing cost.Comment: Genetic and Evolutionary Computation Conference (GECCO'12) (2012
Cutoff for non-backtracking random walks on sparse random graphs
A finite ergodic Markov chain is said to exhibit cutoff if its distance to
stationarity remains close to 1 over a certain number of iterations and then
abruptly drops to near 0 on a much shorter time scale. Discovered in the
context of card shuffling (Aldous-Diaconis, 1986), this phenomenon is now
believed to be rather typical among fast mixing Markov chains. Yet,
establishing it rigorously often requires a challengingly detailed
understanding of the underlying chain. Here we consider non-backtracking random
walks on random graphs with a given degree sequence. Under a general sparsity
condition, we establish the cutoff phenomenon, determine its precise window,
and prove that the (suitably rescaled) cutoff profile approaches a remarkably
simple, universal shape
Fault-Tolerant, but Paradoxical Path-Finding in Physical and Conceptual Systems
We report our initial investigations into reliability and path-finding based
models and propose future areas of interest. Inspired by broken sidewalks
during on-campus construction projects, we develop two models for navigating
this "unreliable network." These are based on a concept of "accumulating risk"
backward from the destination, and both operate on directed acyclic graphs with
a probability of failure associated with each edge. The first serves to
introduce and has faults addressed by the second, more conservative model.
Next, we show a paradox when these models are used to construct polynomials on
conceptual networks, such as design processes and software development life
cycles. When the risk of a network increases uniformly, the most reliable path
changes from wider and longer to shorter and narrower. If we let professional
inexperience--such as with entry level cooks and software developers--represent
probability of edge failure, does this change in path imply that the novice
should follow instructions with fewer "back-up" plans, yet those with
alternative routes should be followed by the expert?Comment: 8 page
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