84 research outputs found
Faster parameterized algorithm for pumpkin vertex deletion set
A directed graph is called a pumpkin if is a union of induced paths
with a common start vertex and a common end vertex , and the internal
vertices of every two paths are disjoint. We give an algorithm that given a
directed graph and an integer , decides whether a pumpkin can be
obtained from by deleting at most vertices. The algorithm runs in
time
Weighted vertex cover on graphs with maximum degree 3
We give a parameterized algorithm for weighted vertex cover on graphs with
maximum degree 3 whose time complexity is , where is the
minimum size of a vertex cover of the input graph
Succinct data structure for dynamic trees with faster queries
Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for
storing an ordinal tree. The structure supports tree queries in either or time, and insertion or deletion of a single node
in time. In this paper we improve the result of Navarro and
Sadakane by reducing the time complexities of some queries (e.g.\ degree and
level\_ancestor) from to
Parameterized algorithm for 3-path vertex cover
In the 3-path vertex cover problem, the input is an undirected graph and
an integer . The goal is to decide whether there is a set of vertices of
size at most such that every path with 3 vertices in contains at least
one vertex of . In this paper we give parameterized algorithm for 3-path
cover whose time complexity is . Our algorithm is faster than
previous algorithms for this problem
An O^*(2.619^k) algorithm for 4-path vertex cover
In the 4-path vertex cover problem, the input is an undirected graph and
an integer . The goal is to decide whether there is a set of vertices of
size at most such that every path with 4 vertices in contains at least
one vertex of . In this paper we give a parameterized algorithm for 4-path
vertex cover whose time complexity is
Succinct representation of labeled trees
We give a representation for labeled ordered trees that supports labeled
queries such as finding the i-th ancestor of a node with a given label. Our
representation is succinct, namely the redundancy is small-o of the optimal
space for storing the tree. This improves the representation of He et al. which
is succinct unless the entropy of the labels is small
Faster parameterized algorithm for Cluster Vertex Deletion
In the Cluster Vertex Deletion problem the input is a graph and an
integer . The goal is to decide whether there is a set of vertices of
size at most such that the deletion of the vertices of from results
a graph in which every connected component is a clique. We give an algorithm
for Cluster Vertex Deletion whose running time is
Faster deterministic parameterized algorithm for k-Path
In the k-Path problem, the input is a directed graph and an integer
, and the goal is to decide whether there is a simple directed path in
with exactly vertices. We give a deterministic algorithm for k-Path
with time complexity . This improves the previously best
deterministic algorithm for this problem of Zehavi [ESA 2015] whose time
complexity is . The technique used by our algorithm can also be
used to obtain faster deterministic algorithms for k-Tree, r-Dimensional
k-Matching, Graph Motif, and Partial Cover
l-path vertex cover is easier than l-hitting set for small l
In the -path vertex cover problem the input is an undirected graph and
an integer . The goal is to decide whether there is a set of vertices of
size at most such that does not contain a path with vertices. In
this paper we give parameterized algorithms for -path vertex cover for , whose time complexities are , , and
, respectively.Comment: arXiv admin note: text overlap with arXiv:1901.0760
Representation of ordered trees with a given degree distribution
The degree distribution of an ordered tree with nodes is , where is the number of nodes in with
children. Let be the number of trees with degree
distribution . We give a data structure that stores an ordered tree
with nodes and degree distribution using bits for every constant . The data
structure answers tree queries in constant time. This improves the current data
structures with lowest space for ordered trees: The structure of Jansson et
al.\ [JCSS 2012] that uses
bits, and the structure of Navarro and Sadakane [TALG 2014] that uses
bits for every constant
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