317 research outputs found
(Total) Vector Domination for Graphs with Bounded Branchwidth
Given a graph of order and an -dimensional non-negative
vector , called demand vector, the vector domination
(resp., total vector domination) is the problem of finding a minimum
such that every vertex in (resp., in ) has
at least neighbors in . The (total) vector domination is a
generalization of many dominating set type problems, e.g., the dominating set
problem, the -tuple dominating set problem (this is different from the
solution size), and so on, and its approximability and inapproximability have
been studied under this general framework. In this paper, we show that a
(total) vector domination of graphs with bounded branchwidth can be solved in
polynomial time. This implies that the problem is polynomially solvable also
for graphs with bounded treewidth. Consequently, the (total) vector domination
problem for a planar graph is subexponential fixed-parameter tractable with
respectto , where is the size of solution.Comment: 16 page
Ground states of a two phase model with cross and self attractive interactions
We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations
A linear algorithm for string reconstruction in the reverse complement equivalence model
In the reverse complement equivalence model, it is not possible to distinguish a string from its reverse complement. We show that one can still reconstruct a string of length n, up to reverse complement, using a linear number of subsequence queries of bounded length. We first give the proof for strings over a binary alphabet, and then extend it to arbitrary finite alphabets. A simple information theoretic lower bound proves the number of queries to be asymptotically tight. Furthermore, our result is optimal w.r.t. the bound on the query length given in Erdos et al. (2006) [6]
Normal, Abby Normal, Prefix Normal
A prefix normal word is a binary word with the property that no substring has
more 1s than the prefix of the same length. This class of words is important in
the context of binary jumbled pattern matching. In this paper we present
results about the number of prefix normal words of length , showing
that for some and
. We introduce efficient
algorithms for testing the prefix normal property and a "mechanical algorithm"
for computing prefix normal forms. We also include games which can be played
with prefix normal words. In these games Alice wishes to stay normal but Bob
wants to drive her "abnormal" -- we discuss which parameter settings allow
Alice to succeed.Comment: Accepted at FUN '1
Parameterized Inapproximability of Target Set Selection and Generalizations
In this paper, we consider the Target Set Selection problem: given a graph
and a threshold value for any vertex of the graph, find a minimum
size vertex-subset to "activate" s.t. all the vertices of the graph are
activated at the end of the propagation process. A vertex is activated
during the propagation process if at least of its neighbors are
activated. This problem models several practical issues like faults in
distributed networks or word-to-mouth recommendations in social networks. We
show that for any functions and this problem cannot be approximated
within a factor of in time, unless FPT = W[P],
even for restricted thresholds (namely constant and majority thresholds). We
also study the cardinality constraint maximization and minimization versions of
the problem for which we prove similar hardness results
Influence Diffusion in Social Networks under Time Window Constraints
We study a combinatorial model of the spread of influence in networks that
generalizes existing schemata recently proposed in the literature. In our
model, agents change behaviors/opinions on the basis of information collected
from their neighbors in a time interval of bounded size whereas agents are
assumed to have unbounded memory in previously studied scenarios. In our
mathematical framework, one is given a network , an integer value
for each node , and a time window size . The goal is to
determine a small set of nodes (target set) that influences the whole graph.
The spread of influence proceeds in rounds as follows: initially all nodes in
the target set are influenced; subsequently, in each round, any uninfluenced
node becomes influenced if the number of its neighbors that have been
influenced in the previous rounds is greater than or equal to .
We prove that the problem of finding a minimum cardinality target set that
influences the whole network is hard to approximate within a
polylogarithmic factor. On the positive side, we design exact polynomial time
algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared
in: Proceedings of 20th International Colloquium on Structural Information
and Communication Complexity (Sirocco 2013), Lectures Notes in Computer
Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201
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