1,537 research outputs found
Editing to Eulerian Graphs
We investigate the problem of modifying a graph into a connected graph in which the degree of each vertex satisfies a prescribed parity constraint. Let ea, ed and vd denote the operations edge addition, edge deletion and vertex deletion respectively. For any S subseteq {ea,ed,vd}, we define Connected Degree Parity Editing (S) (CDPE(S)) to be the problem that takes as input a graph G, an integer k and a function delta: V(G) -> {0,1}, and asks whether G can be modified into a connected graph H with d_H(v) = delta(v)(mod 2) for each v in V(H), using at most k operations from S. We prove that (*) if S={ea} or S={ea,ed}, then CDPE(S) can be solved in polynomial time; (*) if {vd} subseteq S subseteq {ea,ed,vd}, then CDPE(S) is NP-complete and W-hard when parameterized by k, even if delta = 0. Together with known results by Cai and Yang and by Cygan, Marx, Pilipczuk, Pilipczuk and Schlotter, our results completely classify the classical and parameterized complexity of the CDPE(S) problem for all S subseteq {ea,ed,vd}. We obtain the same classification for a natural variant of the cdpe(S) problem on directed graphs, where the target is a weakly connected digraph in which the difference between the in- and out-degree of every vertex equals a prescribed value. As an important implication of our results, we obtain polynomial-time algorithms for Eulerian Editing problem and its directed variant. To the best of our knowledge, the only other natural non-trivial graph class H for which the H-Editing problem is known to be polynomial-time solvable is the class of split graphs
Editing to Eulerian Graphs
We investigate the problem of modifying a graph into a connected graph in which the degree of each vertex satisfies a prescribed parity constraint. Let ea, ed and vd denote the operations edge addition, edge deletion and vertex deletion respectively. For any S subseteq {ea,ed,vd}, we define Connected Degree Parity Editing (S) (CDPE(S)) to be the problem that takes as input a graph G, an integer k and a function delta: V(G) -> {0,1}, and asks whether G can be modified into a connected graph H with d_H(v) = delta(v)(mod 2) for each v in V(H), using at most k operations from S. We prove that (*) if S={ea} or S={ea,ed}, then CDPE(S) can be solved in polynomial time; (*) if {vd} subseteq S subseteq {ea,ed,vd}, then CDPE(S) is NP-complete and W-hard when parameterized by k, even if delta = 0. Together with known results by Cai and Yang and by Cygan, Marx, Pilipczuk, Pilipczuk and Schlotter, our results completely classify the classical and parameterized complexity of the CDPE(S) problem for all S subseteq {ea,ed,vd}. We obtain the same classification for a natural variant of the cdpe(S) problem on directed graphs, where the target is a weakly connected digraph in which the difference between the in- and out-degree of every vertex equals a prescribed value. As an important implication of our results, we obtain polynomial-time algorithms for Eulerian Editing problem and its directed variant. To the best of our knowledge, the only other natural non-trivial graph class H for which the H-Editing problem is known to be polynomial-time solvable is the class of split graphs.publishedVersio
Editing to Eulerian Graphs
We investigate the problem of modifying a graph into a connected graph in
which the degree of each vertex satisfies a prescribed parity constraint. Let
, and denote the operations edge addition, edge deletion and
vertex deletion respectively. For any , we define
Connected Degree Parity Editing (CDPE()) to be the problem that takes
as input a graph , an integer and a function , and asks whether can be modified into a connected
graph with for each , using
at most operations from . We prove that
1. if or , then CDPE() can be solved in polynomial
time;
2. if , then CDPE() is
NP-complete and W[1]-hard when parameterized by , even if .
Together with known results by Cai and Yang and by Cygan, Marx, Pilipczuk,
Pilipczuk and Schlotter, our results completely classify the classical and
parameterized complexity of the CDPE() problem for all . We obtain the same classification for a natural variant of the
CDPE() problem on directed graphs, where the target is a weakly connected
digraph in which the difference between the in- and out-degree of every vertex
equals a prescribed value. As an important implication of our results, we
obtain polynomial-time algorithms for the Eulerian Editing problem and its
directed variant.Comment: 33 pages. An extended abstract of this paper will appear in the
proceedings of FSTTCS 201
Nonlinear dance motion analysis and motion editing using Hilbert-Huang transform
Human motions (especially dance motions) are very noisy, and it is hard to
analyze and edit the motions. To resolve this problem, we propose a new method
to decompose and modify the motions using the Hilbert-Huang transform (HHT).
First, HHT decomposes a chromatic signal into "monochromatic" signals that are
the so-called Intrinsic Mode Functions (IMFs) using an Empirical Mode
Decomposition (EMD) [6]. After applying the Hilbert Transform to each IMF, the
instantaneous frequencies of the "monochromatic" signals can be obtained. The
HHT has the advantage to analyze non-stationary and nonlinear signals such as
human-joint-motions over FFT or Wavelet transform.
In the present paper, we propose a new framework to analyze and extract some
new features from a famous Japanese threesome pop singer group called
"Perfume", and compare it with Waltz and Salsa dance. Using the EMD, their
dance motions can be decomposed into motion (choreographic) primitives or IMFs.
Therefore we can scale, combine, subtract, exchange, and modify those IMFs, and
can blend them into new dance motions self-consistently. Our analysis and
framework can lead to a motion editing and blending method to create a new
dance motion from different dance motions.Comment: 6 pages, 10 figures, Computer Graphics International 2017, Conference
short pape
A survey of parameterized algorithms and the complexity of edge modification
The survey is a comprehensive overview of the developing area of parameterized algorithms for graph modification problems. It describes state of the art in kernelization, subexponential algorithms, and parameterized complexity of graph modification. The main focus is on edge modification problems, where the task is to change some adjacencies in a graph to satisfy some required properties. To facilitate further research, we list many open problems in the area.publishedVersio
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