786 research outputs found
A Planarity Test via Construction Sequences
Optimal linear-time algorithms for testing the planarity of a graph are
well-known for over 35 years. However, these algorithms are quite involved and
recent publications still try to give simpler linear-time tests. We give a
simple reduction from planarity testing to the problem of computing a certain
construction of a 3-connected graph. The approach is different from previous
planarity tests; as key concept, we maintain a planar embedding that is
3-connected at each point in time. The algorithm runs in linear time and
computes a planar embedding if the input graph is planar and a
Kuratowski-subdivision otherwise
Linear Parsing Expression Grammars
PEGs were formalized by Ford in 2004, and have several pragmatic operators
(such as ordered choice and unlimited lookahead) for better expressing modern
programming language syntax. Since these operators are not explicitly defined
in the classic formal language theory, it is significant and still challenging
to argue PEGs' expressiveness in the context of formal language theory.Since
PEGs are relatively new, there are several unsolved problems.One of the
problems is revealing a subclass of PEGs that is equivalent to DFAs. This
allows application of some techniques from the theory of regular grammar to
PEGs. In this paper, we define Linear PEGs (LPEGs), a subclass of PEGs that is
equivalent to DFAs. Surprisingly, LPEGs are formalized by only excluding some
patterns of recursive nonterminal in PEGs, and include the full set of ordered
choice, unlimited lookahead, and greedy repetition, which are characteristic of
PEGs. Although the conversion judgement of parsing expressions into DFAs is
undecidable in general, the formalism of LPEGs allows for a syntactical
judgement of parsing expressions.Comment: Parsing expression grammars, Boolean finite automata, Packrat parsin
Applying MAPP Algorithm for Cooperative Path Finding in Urban Environments
The paper considers the problem of planning a set of non-conflict
trajectories for the coalition of intelligent agents (mobile robots). Two
divergent approaches, e.g. centralized and decentralized, are surveyed and
analyzed. Decentralized planner - MAPP is described and applied to the task of
finding trajectories for dozens UAVs performing nap-of-the-earth flight in
urban environments. Results of the experimental studies provide an opportunity
to claim that MAPP is a highly efficient planner for solving considered types
of tasks
A Fast Algorithm for Enumerating Bipartite Perfect Matchings
Abstract: In this paper, we propose an algorithm for enumerating all the perfect matchings included in a given bipartite graph G =(V,E). The algorithm is improved by the approach which we proposed at ISAAC98. Our algorithm takes O(log |V |) time per perfect matching while the current fastest algorithm takes O(|V |) time per perfect matching
Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons
We consider the following motion-planning problem: we are given unit
discs in a simple polygon with vertices, each at their own start position,
and we want to move the discs to a given set of target positions. Contrary
to the standard (labeled) version of the problem, each disc is allowed to be
moved to any target position, as long as in the end every target position is
occupied. We show that this unlabeled version of the problem can be solved in
time, assuming that the start and target positions are at
least some minimal distance from each other. This is in sharp contrast to the
standard (labeled) and more general multi-robot motion-planning problem for
discs moving in a simple polygon, which is known to be strongly NP-hard
Space Complexity of Stack Automata Models
This paper examines several measures of space complexity on variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept any word in a language (weak measure), the maximum stack size used in any accepting computation on any accepted word (accept measure), and the maximum stack size used in any computation (strong measure). We give a detailed characterization of the accept and strong space complexity measures for checking stack automata. Exactly one of three cases can occur: the complexity is either bounded by a constant, behaves (up to small technicalities explained in the paper) like a linear function, or it grows arbitrarily larger than the length of the input word. However, this result does not hold for non-erasing stack automata; we provide an example when the space complexity grows with the square root of the input length. Furthermore, an investigation is done regarding the best complexity of any machine accepting a given language, and on decidability of space complexity properties
On Lebesgue measure of integral self-affine sets
Let be an expanding integer matrix and be a finite subset
of . The self-affine set is the unique compact set satisfying
the equality . We present an effective algorithm to
compute the Lebesgue measure of the self-affine set , the measure of
intersection for , and the measure of intersection of
self-affine sets for different sets .Comment: 5 pages, 1 figur
On the Shuffle Automaton Size for Words
We investigate the state size of DFAs accepting the shuffle of two words. We
provide words u and v, such that the minimal DFA for u shuffled with v requires
an exponential number of states. We also show some conditions for the words u
and v which ensure a quadratic upper bound on the state size of u shuffled with
v. Moreover, switching only two letters within one of u or v is enough to
trigger the change from quadratic to exponential
Serializing the Parallelism in Parallel Communicating Pushdown Automata Systems
We consider parallel communicating pushdown automata systems (PCPA) and
define a property called known communication for it. We use this property to
prove that the power of a variant of PCPA, called returning centralized
parallel communicating pushdown automata (RCPCPA), is equivalent to that of
multi-head pushdown automata. The above result presents a new sub-class of
returning parallel communicating pushdown automata systems (RPCPA) called
simple-RPCPA and we show that it can be written as a finite intersection of
multi-head pushdown automata systems
Deep Manifold Traversal: Changing Labels with Convolutional Features
Many tasks in computer vision can be cast as a "label changing" problem, where the goal is to make a semantic change to the appearance of an image or some subject in an image in order to alter the class membership. Although successful task-specific methods have been developed for some label changing applications, to date no general purpose method exists. Motivated by this we propose deep manifold traversal, a method that addresses the problem in its most general form: it first approximates the manifold of natural images then morphs a test image along a traversal path away from a source class and towards a target class while staying near the manifold throughout. The resulting algorithm is surprisingly effective and versatile. It is completely data driven, requiring only an example set of images from the desired source and target domains. We demonstrate deep manifold traversal on highly diverse label changing tasks: changing an individual's appearance (age and hair color), changing the season of an outdoor image, and transforming a city skyline towards nighttime
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