2,423 research outputs found
Domination Cover Pebbling: Structural Results
This paper continues the results of "Domination Cover Pebbling: Graph
Families." An almost sharp bound for the domination cover pebbling (DCP) number
for graphs G with specified diameter has been computed. For graphs of diameter
two, a bound for the ratio between the cover pebbling number of G and the DCP
number of G has been computed. A variant of domination cover pebbling, called
subversion DCP is introducted, and preliminary results are discussed.Comment: 15 page
From Bandits to Experts: A Tale of Domination and Independence
We consider the partial observability model for multi-armed bandits,
introduced by Mannor and Shamir. Our main result is a characterization of
regret in the directed observability model in terms of the dominating and
independence numbers of the observability graph. We also show that in the
undirected case, the learner can achieve optimal regret without even accessing
the observability graph before selecting an action. Both results are shown
using variants of the Exp3 algorithm operating on the observability graph in a
time-efficient manner
Uniqueness and non-uniqueness in percolation theory
This paper is an up-to-date introduction to the problem of uniqueness versus
non-uniqueness of infinite clusters for percolation on and,
more generally, on transitive graphs. For iid percolation on ,
uniqueness of the infinite cluster is a classical result, while on certain
other transitive graphs uniqueness may fail. Key properties of the graphs in
this context turn out to be amenability and nonamenability. The same problem is
considered for certain dependent percolation models -- most prominently the
Fortuin--Kasteleyn random-cluster model -- and in situations where the standard
connectivity notion is replaced by entanglement or rigidity. So-called
simultaneous uniqueness in couplings of percolation processes is also
considered. Some of the main results are proved in detail, while for others the
proofs are merely sketched, and for yet others they are omitted. Several open
problems are discussed.Comment: Published at http://dx.doi.org/10.1214/154957806000000096 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A new approach on locally checkable problems
By providing a new framework, we extend previous results on locally checkable
problems in bounded treewidth graphs. As a consequence, we show how to solve,
in polynomial time for bounded treewidth graphs, double Roman domination and
Grundy domination, among other problems for which no such algorithm was
previously known. Moreover, by proving that fixed powers of bounded degree and
bounded treewidth graphs are also bounded degree and bounded treewidth graphs,
we can enlarge the family of problems that can be solved in polynomial time for
these graph classes, including distance coloring problems and distance
domination problems (for bounded distances)
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