1,586 research outputs found
Arboreal Bound Entanglement
In this paper, we discuss the entanglement properties of graph-diagonal
states, with particular emphasis on calculating the threshold for the
transition between the presence and absence of entanglement (i.e. the
separability point). Special consideration is made of the thermal states of
trees, including the linear cluster state. We characterise the type of
entanglement present, and describe the optimal entanglement witnesses and their
implementation on a quantum computer, up to an additive approximation. In the
case of general graphs, we invoke a relation with the partition function of the
classical Ising model, thereby intimating a connection to computational
complexity theoretic tasks. Finally, we show that the entanglement is robust to
some classes of local perturbations.Comment: 9 pages + appendices, 3 figure
The Complexity of Matching Games: A Survey
Matching games naturally generalize assignment games, a well-known class of
cooperative games. Interest in matching games has grown recently due to some
breakthrough results and new applications. This state-of-the-art survey
provides an overview of matching games and extensions, such as -matching
games and partitioned matching games; the latter originating from the emerging
area of international kidney exchange. In this survey we focus on computational
complexity aspects of various game-theoretical solution concepts, such as the
core, nucleolus and Shapley value, when the input is restricted to some
(generalized) matching game
Photothermal characterization of encapsulant materials for photovoltaic modules
A photothermal test matrix and a low cost testing apparatus for encapsulant materials of photovoltaic modules were defined. Photothermal studies were conducted to screen and rank existing as well as future encapsulant candidate materials and/or material formulations in terms of their long term physiochemical stability under accelerated photothermal aging conditions. Photothermal characterization of six candidate pottant materials and six candidate outer cover materials were carried out. Principal products of photothermal degradation are identified. Certain critical properties are also monitored as a function of photothermal aging
Stabilizing Weighted Graphs
An edge-weighted graph G=(V,E) is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as network bargaining games and cooperative matching games, because they characterize instances which admit stable outcomes. Motivated by this, in the last few years many researchers have investigated the algorithmic problem of turning a given graph into a stable one, via edge- and vertex-removal operations. However, all the algorithmic results developed in the literature so far only hold for unweighted instances, i.e., assuming unit weights on the edges of G.
We give the first polynomial-time algorithm to find a minimum cardinality subset of vertices whose removal from G yields a stable graph, for any weighted graph G. The algorithm is combinatorial and exploits new structural properties of basic fractional matchings, which are of independent interest. In particular, one of the main ingredients of our result is the development of a polynomial-time algorithm to compute a basic maximum-weight fractional matching with minimum number of odd cycles in its support. This generalizes a fundamental and classical result on unweighted matchings given by Balas more than 30 years ago, which we expect to prove useful beyond this particular application.
In contrast, we show that the problem of finding a minimum cardinality subset of edges whose removal from a weighted graph G yields a stable graph, does not admit any constant-factor approximation algorithm, unless P=NP. In this setting, we develop an O(Delta)-approximation algorithm for the problem, where Delta is the maximum degree of a node in G
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