1,153 research outputs found
The Computational Complexity of the Game of Set and its Theoretical Applications
The game of SET is a popular card game in which the objective is to form Sets
using cards from a special deck. In this paper we study single- and multi-round
variations of this game from the computational complexity point of view and
establish interesting connections with other classical computational problems.
Specifically, we first show that a natural generalization of the problem of
finding a single Set, parameterized by the size of the sought Set is W-hard;
our reduction applies also to a natural parameterization of Perfect
Multi-Dimensional Matching, a result which may be of independent interest.
Second, we observe that a version of the game where one seeks to find the
largest possible number of disjoint Sets from a given set of cards is a special
case of 3-Set Packing; we establish that this restriction remains NP-complete.
Similarly, the version where one seeks to find the smallest number of disjoint
Sets that overlap all possible Sets is shown to be NP-complete, through a close
connection to the Independent Edge Dominating Set problem. Finally, we study a
2-player version of the game, for which we show a close connection to Arc
Kayles, as well as fixed-parameter tractability when parameterized by the
number of rounds played
Expanding the expressive power of Monadic Second-Order logic on restricted graph classes
We combine integer linear programming and recent advances in Monadic
Second-Order model checking to obtain two new algorithmic meta-theorems for
graphs of bounded vertex-cover. The first shows that cardMSO1, an extension of
the well-known Monadic Second-Order logic by the addition of cardinality
constraints, can be solved in FPT time parameterized by vertex cover. The
second meta-theorem shows that the MSO partitioning problems introduced by Rao
can also be solved in FPT time with the same parameter. The significance of our
contribution stems from the fact that these formalisms can describe problems
which are W[1]-hard and even NP-hard on graphs of bounded tree-width.
Additionally, our algorithms have only an elementary dependence on the
parameter and formula. We also show that both results are easily extended from
vertex cover to neighborhood diversity.Comment: Accepted for IWOCA 201
Cell division in apicomplexan parasites is organized by a homolog of the striated rootlet fiber of algal flagella
Apicomplexa are intracellular parasites that cause important human diseases including malaria and toxoplasmosis. During host cell infection new parasites are formed through a budding process that parcels out nuclei and organelles into multiple daughters. Budding is remarkably flexible in output and can produce two to thousands of progeny cells. How genomes and daughters are counted and coordinated is unknown. Apicomplexa evolved from single celled flagellated algae, but with the exception of the gametes, lack flagella. Here we demonstrate that a structure that in the algal ancestor served as the rootlet of the flagellar basal bodies is required for parasite cell division. Parasite striated fiber assemblins (SFA) polymerize into a dynamic fiber that emerges from the centrosomes immediately after their duplication. The fiber grows in a polarized fashion and daughter cells form at its distal tip. As the daughter cell is further elaborated it remains physically tethered at its apical end, the conoid and polar ring. Genetic experiments in Toxoplasma gondii demonstrate two essential components of the fiber, TgSFA2 and 3. In the absence of either of these proteins cytokinesis is blocked at its earliest point, the initiation of the daughter microtubule organizing center (MTOC). Mitosis remains unimpeded and mutant cells accumulate numerous nuclei but fail to form daughter cells. The SFA fiber provides a robust spatial and temporal organizer of parasite cell division, a process that appears hard-wired to the centrosome by multiple tethers. Our findings have broader evolutionary implications. We propose that Apicomplexa abandoned flagella for most stages yet retained the organizing principle of the flagellar MTOC. Instead of ensuring appropriate numbers of flagella, the system now positions the apical invasion complexes. This suggests that elements of the invasion apparatus may be derived from flagella or flagellum associated structures
Parameterized Algorithms for Modular-Width
It is known that a number of natural graph problems which are FPT
parameterized by treewidth become W-hard when parameterized by clique-width. It
is therefore desirable to find a different structural graph parameter which is
as general as possible, covers dense graphs but does not incur such a heavy
algorithmic penalty.
The main contribution of this paper is to consider a parameter called
modular-width, defined using the well-known notion of modular decompositions.
Using a combination of ILPs and dynamic programming we manage to design FPT
algorithms for Coloring and Partitioning into paths (and hence Hamiltonian path
and Hamiltonian cycle), which are W-hard for both clique-width and its recently
introduced restriction, shrub-depth. We thus argue that modular-width occupies
a sweet spot as a graph parameter, generalizing several simpler notions on
dense graphs but still evading the "price of generality" paid by clique-width.Comment: to appear in IPEC 2013. arXiv admin note: text overlap with
arXiv:1304.5479 by other author
Parameterized Approximation Schemes using Graph Widths
Combining the techniques of approximation algorithms and parameterized
complexity has long been considered a promising research area, but relatively
few results are currently known. In this paper we study the parameterized
approximability of a number of problems which are known to be hard to solve
exactly when parameterized by treewidth or clique-width. Our main contribution
is to present a natural randomized rounding technique that extends well-known
ideas and can be used for both of these widths. Applying this very generic
technique we obtain approximation schemes for a number of problems, evading
both polynomial-time inapproximability and parameterized intractability bounds
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