8,109 research outputs found
An Exponential Lower Bound for the Latest Deterministic Strategy Iteration Algorithms
This paper presents a new exponential lower bound for the two most popular
deterministic variants of the strategy improvement algorithms for solving
parity, mean payoff, discounted payoff and simple stochastic games. The first
variant improves every node in each step maximizing the current valuation
locally, whereas the second variant computes the globally optimal improvement
in each step. We outline families of games on which both variants require
exponentially many strategy iterations
Symmetric Strategy Improvement
Symmetry is inherent in the definition of most of the two-player zero-sum
games, including parity, mean-payoff, and discounted-payoff games. It is
therefore quite surprising that no symmetric analysis techniques for these
games exist. We develop a novel symmetric strategy improvement algorithm where,
in each iteration, the strategies of both players are improved simultaneously.
We show that symmetric strategy improvement defies Friedmann's traps, which
shook the belief in the potential of classic strategy improvement to be
polynomial
A tabu search procedure for generating robust project baseline schedules under stochastic resource availabilities.
The majority of research efforts in project scheduling assume a static and deterministic environment with complete information. In practice, however, these assumptions will hardly, if ever, be satisfied. Proactive scheduling aims at the generation of robust baseline schedules that are as much as possible protected against anticipated disruptions that may occur during project execution. In this paper, we focus on disruptions that may be caused by stochastic resource availabilities and aim at generating stable baseline schedules, where the solution robustness (stability) of the baseline schedule is measured by the weighted deviation between the planned and the actually realized activity starting times during project execution. We present a tabu search procedure that operates on a surrogate free slack based objective function. The effectiveness of the procedure is demonstrated by extensive computational results obtained on a set of randomly generated test instances.
A tabu search procedure for developing robust predicitive project schedules.
Proactive scheduling aims at the generation of robust baseline schedules that are as much as possible protected against disruptions that may occur during project execution. In this paper, we focus on disruptions caused by stochastic resource availabilities and aim at generating stable baseline schedules. A schedule’s robustness (stability) is measured by the weighted deviation between the planned and the actually realized activity starting times during project execution. We present a tabu search procedure that operates on a surrogate, free slack based objective function. Its effectiveness is demonstrated by extensive computational results obtained on a set of randomly generated test instances.Project scheduling; Robustness; Proactive; Stability;
Global Continuous Optimization with Error Bound and Fast Convergence
This paper considers global optimization with a black-box unknown objective
function that can be non-convex and non-differentiable. Such a difficult
optimization problem arises in many real-world applications, such as parameter
tuning in machine learning, engineering design problem, and planning with a
complex physics simulator. This paper proposes a new global optimization
algorithm, called Locally Oriented Global Optimization (LOGO), to aim for both
fast convergence in practice and finite-time error bound in theory. The
advantage and usage of the new algorithm are illustrated via theoretical
analysis and an experiment conducted with 11 benchmark test functions. Further,
we modify the LOGO algorithm to specifically solve a planning problem via
policy search with continuous state/action space and long time horizon while
maintaining its finite-time error bound. We apply the proposed planning method
to accident management of a nuclear power plant. The result of the application
study demonstrates the practical utility of our method
Online unit clustering in higher dimensions
We revisit the online Unit Clustering and Unit Covering problems in higher
dimensions: Given a set of points in a metric space, that arrive one by
one, Unit Clustering asks to partition the points into the minimum number of
clusters (subsets) of diameter at most one; while Unit Covering asks to cover
all points by the minimum number of balls of unit radius. In this paper, we
work in using the norm.
We show that the competitive ratio of any online algorithm (deterministic or
randomized) for Unit Clustering must depend on the dimension . We also give
a randomized online algorithm with competitive ratio for Unit
Clustering}of integer points (i.e., points in , , under norm). We show that the competitive ratio of
any deterministic online algorithm for Unit Covering is at least . This
ratio is the best possible, as it can be attained by a simple deterministic
algorithm that assigns points to a predefined set of unit cubes. We complement
these results with some additional lower bounds for related problems in higher
dimensions.Comment: 15 pages, 4 figures. A preliminary version appeared in the
Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA
2017
The Fixpoint-Iteration Algorithm for Parity Games
It is known that the model checking problem for the modal mu-calculus reduces
to the problem of solving a parity game and vice-versa. The latter is realised
by the Walukiewicz formulas which are satisfied by a node in a parity game iff
player 0 wins the game from this node. Thus, they define her winning region,
and any model checking algorithm for the modal mu-calculus, suitably
specialised to the Walukiewicz formulas, yields an algorithm for solving parity
games. In this paper we study the effect of employing the most straight-forward
mu-calculus model checking algorithm: fixpoint iteration. This is also one of
the few algorithms, if not the only one, that were not originally devised for
parity game solving already. While an empirical study quickly shows that this
does not yield an algorithm that works well in practice, it is interesting from
a theoretical point for two reasons: first, it is exponential on virtually all
families of games that were designed as lower bounds for very particular
algorithms suggesting that fixpoint iteration is connected to all those.
Second, fixpoint iteration does not compute positional winning strategies. Note
that the Walukiewicz formulas only define winning regions; some additional work
is needed in order to make this algorithm compute winning strategies. We show
that these are particular exponential-space strategies which we call
eventually-positional, and we show how positional ones can be extracted from
them.Comment: In Proceedings GandALF 2014, arXiv:1408.556
The streaming -mismatch problem
We consider the streaming complexity of a fundamental task in approximate
pattern matching: the -mismatch problem. It asks to compute Hamming
distances between a pattern of length and all length- substrings of a
text for which the Hamming distance does not exceed a given threshold . In
our problem formulation, we report not only the Hamming distance but also, on
demand, the full \emph{mismatch information}, that is the list of mismatched
pairs of symbols and their indices. The twin challenges of streaming pattern
matching derive from the need both to achieve small working space and also to
guarantee that every arriving input symbol is processed quickly.
We present a streaming algorithm for the -mismatch problem which uses
bits of space and spends \ourcomplexity time on
each symbol of the input stream, which consists of the pattern followed by the
text. The running time almost matches the classic offline solution and the
space usage is within a logarithmic factor of optimal.
Our new algorithm therefore effectively resolves and also extends an open
problem first posed in FOCS'09. En route to this solution, we also give a
deterministic -bit encoding of all
the alignments with Hamming distance at most of a length- pattern within
a text of length . This secondary result provides an optimal solution to
a natural communication complexity problem which may be of independent
interest.Comment: 27 page
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