Sharing Non-Anonymous Costs of Multiple Resources Optimally

In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs. We consider a general class of resource allocation problems in which a set of resources is used by a heterogeneous set of selfish users. The cost of a resource is a (non-decreasing) function of the set of its users. Under the assumption that the costs of the resources are shared by uniform cost sharing protocols, i.e., protocols that use only local information of the resource's cost structure and its users to determine the cost shares, we exactly quantify the inefficiency of the resulting pure Nash equilibria. Specifically, we show tight bounds on prices of stability and anarchy for games with only submodular and only supermodular cost functions, respectively, and an asymptotically tight bound for games with arbitrary set-functions. While all our upper bounds are attained for the well-known Shapley cost sharing protocol, our lower bounds hold for arbitrary uniform cost sharing protocols and are even valid for games with anonymous costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users

Information Flow in Secret Sharing Protocols

The entangled graph states have emerged as an elegant and powerful quantum resource, indeed almost all multiparty protocols can be written in terms of graph states including measurement based quantum computation (MBQC), error correction and secret sharing amongst others. In addition they are at the forefront in terms of implementations. As such they represent an excellent opportunity to move towards integrated protocols involving many of these elements. In this paper we look at expressing and extending graph state secret sharing and MBQC in a common framework and graphical language related to flow. We do so with two main contributions. First we express in entirely graphical terms which set of players can access which information in graph state secret sharing protocols. These succinct graphical descriptions of access allow us to take known results from graph theory to make statements on the generalisation of the previous schemes to present new secret sharing protocols. Second, we give a set of necessary conditions as to when a graph with flow, i.e. capable of performing a class of unitary operations, can be extended to include vertices which can be ignored, pointless measurements, and hence considered as unauthorised players in terms of secret sharing, or error qubits in terms of fault tolerance. This offers a way to extend existing MBQC patterns to secret sharing protocols. Our characterisation of pointless measurements is believed also to be a useful tool for further integrated measurement based schemes, for example in constructing fault tolerant MBQC schemes

Absolutely Maximally Entangled States: Existence and Applications

We investigate absolutely maximally entangled (AME) states, which are multipartite quantum states that are maximally entangled with respect to any possible bipartition. These strong entanglement properties make them a powerful resource for a variety of quantum information protocols. In this paper, we show the existence of AME states for any number of parties, given that the dimension of the involved systems is chosen appropriately. We prove the equivalence of AME states shared between an even number of parties and pure state threshold quantum secret sharing (QSS) schemes, and prove necessary and sufficient entanglement properties for a wider class of ramp QSS schemes. We further show how AME states can be used as a valuable resource for open-destination teleportation protocols and to what extend entanglement swapping generalizes to AME states

Quantifying the resource of sharing a reference frame

We define a new quantity called refbit, which allows one to quantify the resource of sharing a reference frame in quantum communication protocols. By considering both asymptotic and nonasymptotic protocols we find relations between refbits and other communication resources. We also consider the same resources in encoded, reference-frame independent, form. This allows one to rephrase and unify previous work on phase references, reference frames, and superselection rules.Comment: Updated title as PRA did not accept the word "refbit" in the title: PRA accepts neither neologisms (="a meaningless word coined by a psychotic", according to Webster), nor novophasm

Resource-Aware Protocols for Network Cost-Sharing Games

We study the extent to which decentralized cost-sharing protocols can achieve good price of anarchy (PoA) bounds in network cost-sharing games with $n$ agents. We focus on the model of resource-aware protocols, where the designer has prior access to the network structure and can also increase the total cost of an edge(overcharging), and we study classes of games with concave or convex cost functions. We first consider concave cost functions and our main result is a cost-sharing protocol for symmetric games on directed acyclic graphs that achieves a PoA of $2+\varepsilon$ for some arbitrary small positive $\varepsilon$, which improves to $1+\varepsilon$ for games with at least two players. We also achieve a PoA of 1 for series-parallel graphs and show that no protocol can achieve a PoA better than $\Omega(\sqrt{n})$ for multicast games. We then also consider convex cost functions and prove analogous results for series-parallel networks and multicast games, as well as a lower bound of $\Omega(n)$ for the PoA on directed acyclic graphs without the use of overcharging

Federal Taxation: Formal Stockholder Vote Held Controlling in Determining When a Plan of Liquidation Is Adopted Under Section 337 of the Internal Revenue Code of 1954

The correctness  of real-time systems does not only depend on the validity of the output, but also the temporal validity. Tasks are typically designed with strict deadlines and they need to respond in time, which are the timing constraints of real-time systems. Schedulability analysis is one of the approaches to study the workload of the task system. DRTRS (Digraph Real-Time task model with resource  sharing) is introduced to describe the system task model, abstracting away most functional behaviour and focus on the timing properties. We have also developed an efficient schedulability analysis under different resource  access protocols

Opaque analysis for resource-sharing components in hierarchical real-time systems : extended version

A real-time component may be developed under the assumption that it has the entire platform at its disposal. Composing a real-time system from independently developed components may require resource sharing between components. We propose opaque analysis methods to integrate resource-sharing components into hierarchically scheduled systems. Resource sharing imposes blocking times within an individual component and between components. An opaque local analysis ignores global blocking between components and allows to analyse an individual component while assuming that shared resources are exclusively available for a component. To arbitrate mutually exclusive resource access between components, we consider four existing protocols: SIRAP, BROE and HSRP - comprising overrun with payback (OWP) and overrun without payback (ONP). We classify local analyses for each synchronization protocol based on the notion of opacity and we develop new analysis for those protocols that are non-opaque. Finally, we compare SIRAP, ONP, OWP and BROE by means of an extensive simulation study. From the results, we derive guidelines for selecting a global synchronization protocol

Designing cost-sharing methods for Bayesian games

We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players