188 research outputs found
Bidimensionality of Geometric Intersection Graphs
Let B be a finite collection of geometric (not necessarily convex) bodies in
the plane. Clearly, this class of geometric objects naturally generalizes the
class of disks, lines, ellipsoids, and even convex polygons. We consider
geometric intersection graphs GB where each body of the collection B is
represented by a vertex, and two vertices of GB are adjacent if the
intersection of the corresponding bodies is non-empty. For such graph classes
and under natural restrictions on their maximum degree or subgraph exclusion,
we prove that the relation between their treewidth and the maximum size of a
grid minor is linear. These combinatorial results vastly extend the
applicability of all the meta-algorithmic results of the bidimensionality
theory to geometrically defined graph classes
Planar graph coloring avoiding monochromatic subgraphs: trees and paths make things difficult
We consider the problem of coloring a planar graph with the minimum number of colors such that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem
Backbone colorings for networks: tree and path backbones
We introduce and study backbone colorings, a variation on classical vertex colorings: Given a graph and a spanning subgraph of (the backbone of ), a backbone coloring for and is a proper vertex coloring of in which the colors assigned to adjacent vertices in differ by at least two. We study the cases where the backbone is either a spanning tree or a spanning path
Connecting Terminals and 2-Disjoint Connected Subgraphs
Given a graph and a set of terminal vertices we say that a
superset of is -connecting if induces a connected graph, and
is minimal if no strict subset of is -connecting. In this paper we prove
that there are at most minimal -connecting sets when and that
these can be enumerated within a polynomial factor of this bound. This
generalizes the algorithm for enumerating all induced paths between a pair of
vertices, corresponding to the case . We apply our enumeration algorithm
to solve the {\sc 2-Disjoint Connected Subgraphs} problem in time
, improving on the recent algorithm of Cygan et
al. 2012 LATIN paper.Comment: 13 pages, 1 figur
Efficient Exact Algorithms on Planar Graphs: Exploiting Sphere Cut Decompositions
A divide-and-conquer strategy based on variations of the Lipton-Tarjan planar separator
theorem has been one of the most common approaches for solving planar graph problems for
more than 20 years. We present a new framework for designing fast subexponential exact and parameterized algorithms on planar graphs. Our approach is based on geometric properties of planar branch decompositions obtained by Seymour & Thomas, combined with refined techniques of dynamic programming on planar graphs based on properties of non-crossing partitions. Compared to divide-and-conquer algorithms, the main advantages of our method are a) it is a generic method which allows to attack broad classes of problems; b) the obtained algorithms provide a better worst case analysis. To exemplify our approach we show how to obtain an O(26.903√n) time algorithm solving weighted HAMILTONIAN CYCLE. We observe how our technique can be used to solve PLANAR GRAPH TSP in time O(29.8594√n). Our approach can be used to design parameterized algorithms as well. For example we introduce the first 2O(√ k)nO(1) time algorithm for parameterized Planar k-cycle by showing that for a given k we can decide if a planar graph on n vertices has a cycle of length at least k in time O(213.6√kn + n3)
Planar graph coloring avoiding monochromatic subgraphs : trees and paths make it difficult
We consider the problem of coloring a planar graph with the minimum number of colors so that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem. We present a complete picture for the case with a single forbidden connected (induced or noninduced) subgraph. The 2-coloring problem is NP-hard if the forbidden subgraph is a tree with at least two edges, and it is polynomially solvable in all other cases. The 3-coloring problem is NP-hard if the forbidden subgraph is a path with at least one edge, and it is polynomially solvable in all other cases. We also derive results for several forbidden sets of cycles. In particular, we prove that it is NP-complete to decide if a planar graph can be 2-colored so that no cycle of length at most 5 is monochromatic
Feedback Vertex Sets in Tournaments
We study combinatorial and algorithmic questions around minimal feedback
vertex sets in tournament graphs.
On the combinatorial side, we derive strong upper and lower bounds on the
maximum number of minimal feedback vertex sets in an n-vertex tournament. We
prove that every tournament on n vertices has at most 1.6740^n minimal feedback
vertex sets, and that there is an infinite family of tournaments, all having at
least 1.5448^n minimal feedback vertex sets. This improves and extends the
bounds of Moon (1971).
On the algorithmic side, we design the first polynomial space algorithm that
enumerates the minimal feedback vertex sets of a tournament with polynomial
delay. The combination of our results yields the fastest known algorithm for
finding a minimum size feedback vertex set in a tournament
An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure
The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for
the traveling salesman problem in an n-vertex graph with maximum degree 3. This
improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and
O^*(1.260^n) by Eppstein. Our algorithm is a simple branch-and-search
algorithm. The only branch rule is designed on a cut-circuit structure of a
graph induced by unprocessed edges. To improve a time bound by a simple
analysis on measure and conquer, we introduce an amortization scheme over the
cut-circuit structure by defining the measure of an instance to be the sum of
not only weights of vertices but also weights of connected components of the
induced graph.Comment: 24 pages and 4 figure
Assigning channels via the meet-in-the-middle approach
We study the complexity of the Channel Assignment problem. By applying the
meet-in-the-middle approach we get an algorithm for the -bounded Channel
Assignment (when the edge weights are bounded by ) running in time
. This is the first algorithm which breaks the
barrier. We extend this algorithm to the counting variant, at the
cost of slightly higher polynomial factor.
A major open problem asks whether Channel Assignment admits a -time
algorithm, for a constant independent of . We consider a similar
question for Generalized T-Coloring, a CSP problem that generalizes \CA. We
show that Generalized T-Coloring does not admit a
-time algorithm, where is the
size of the instance.Comment: SWAT 2014: 282-29
Electric-dipole active two-magnon excitation in {\textit{ab}} spiral spin phase of a ferroelectric magnet GdTbMnO
A broad continuum-like spin excitation (1--10 meV) with a peak structure
around 2.4 meV has been observed in the ferroelectric spiral spin phase of
GdTbMnO by using terahertz (THz) time-domain spectroscopy.
Based on a complete set of light-polarization measurements, we identify the
spin excitation active for the light vector only along the a-axis, which
grows in intensity with lowering temperature even from above the magnetic
ordering temperature but disappears upon the transition to the -type
antiferromagnetic phase. Such an electric-dipole active spin excitation as
observed at THz frequencies can be ascribed to the two-magnon excitation in
terms of the unique polarization selection rule in a variety of the
magnetically ordered phases.Comment: 11 pages including 3 figure
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