Quantum Lower Bounds for Fanout

We prove several new lower bounds for constant depth quantum circuits. The main result is that parity (and hence fanout) requires log depth circuits, when the circuits are composed of single qubit and arbitrary size Toffoli gates, and when they use only constantly many ancillae. Under this constraint, this bound is close to optimal. In the case of a non-constant number of ancillae, we give a tradeoff between the number of ancillae and the required depth.

Bounds on the Power of Constant-Depth Quantum Circuits

We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, our results imply EQNC^0 ⊆ P, where EQNC^0 is the constant-depth analog of the class EQP. On the other hand, we adapt and extend ideas of Terhal and DiVincenzo [?] to show that, for any family

Cache-and-Relay Streaming Media Delivery for Asynchronous Clients

We consider the problem of delivering popular streaming media to a large number of asynchronous clients. We propose and evaluate a cache-and-relay end-system multicast approach, whereby a client joining a multicast session caches the stream, and if needed, relays that stream to neighboring clients which may join the multicast session at some later time. This cache-and-relay approach is fully distributed, scalable, and efficient in terms of network link cost. In this paper we analytically derive bounds on the network link cost of our cache-and-relay approach, and we evaluate its performance under assumptions of limited client bandwidth and limited client cache capacity. When client bandwidth is limited, we show that although finding an optimal solution is NP-hard, a simple greedy algorithm performs surprisingly well in that it incurs network link costs that are very close to a theoretical lower bound. When client cache capacity is limited, we show that our cache-and-relay approach can still significantly reduce network link cost. We have evaluated our cache-and-relay approach using simulations over large, synthetic random networks, power-law degree networks, and small-world networks, as well as over large real router-level Internet maps.

Collocation Games and Their Application to Distributed Resource Management

We introduce Collocation Games as the basis of a general framework for modeling, analyzing, and facilitating the interactions between the various stakeholders in distributed systems in general, and in cloud computing environments in particular. Cloud computing enables fixed-capacity (processing, communication, and storage) resources to be offered by infrastructure providers as commodities for sale at a fixed cost in an open marketplace to independent, rational parties (players) interested in setting up their own applications over the Internet. Virtualization technologies enable the partitioning of such fixed-capacity resources so as to allow each player to dynamically acquire appropriate fractions of the resources for unencumbered use. In such a paradigm, the resource management problem reduces to that of partitioning the entire set of applications (players) into subsets, each of which is assigned to fixed-capacity cloud resources. If the infrastructure and the various applications are under a single administrative domain, this partitioning reduces to an optimization problem whose objective is to minimize the overall deployment cost. In a marketplace, in which the infrastructure provider is interested in maximizing its own profit, and in which each player is interested in minimizing its own cost, it should be evident that a global optimization is precisely the wrong framework. Rather, in this paper we use a game-theoretic framework in which the assignment of players to fixed-capacity resources is the outcome of a strategic "Collocation Game". Although we show that determining the existence of an equilibrium for collocation games in general is NP-hard, we present a number of simplified, practically-motivated variants of the collocation game for which we establish convergence to a Nash Equilibrium, and for which we derive convergence and price of anarchy bounds. In addition to these analytical results, we present an experimental evaluation of implementations of some of these variants for cloud infrastructures consisting of a collection of multidimensional resources of homogeneous or heterogeneous capacities. Experimental results using trace-driven simulations and synthetically generated datasets corroborate our analytical results and also illustrate how collocation games offer a feasible distributed resource management alternative for autonomic/self-organizing systems, in which the adoption of a global optimization approach (centralized or distributed) would be neither practical nor justifiable.

On Finding Sensitivity of Quantum and Classical Gates

We consider a fault model of Boolean gates, both classical and quantum, where some of the inputs may not be connected to the actual gate hardware. This model is somewhat similar to the stuck-at model which is a very popular model in testing Boolean circuits. We consider the problem of detecting such faults; the detection algorithm can query the faulty gate and its complexity is the number of such queries. This problem is related to determining the sensitivity of Boolean functions. We show how quantum parallelism can be used to detect such faults. Specifically, we show that a quantum algorithm can detect such faults more efficiently than a classical algorithm for a Parity gate and an AND gate. We give explicit constructions of quantum detector algorithms and show lower bounds for classical algorithms. We show that the model for detecting such faults is similar to algebraic decision trees and extend some known results from quantum query complexity to prove some of our results.

Amorphous Placement and Retrieval of Sensory Data in Sparse Mobile Ad-Hoc Networks

Abstract—Personal communication devices are increasingly being equipped with sensors that are able to passively collect information from their surroundings – information that could be stored in fairly small local caches. We envision a system in which users of such devices use their collective sensing, storage, and communication resources to query the state of (possibly remote) neighborhoods. The goal of such a system is to achieve the highest query success ratio using the least communication overhead (power). We show that the use of Data Centric Storage (DCS), or directed placement, is a viable approach for achieving this goal, but only when the underlying network is well connected. Alternatively, we propose, amorphous placement, in which sensory samples are cached locally and informed exchanges of cached samples is used to diffuse the sensory data throughout the whole network. In handling queries, the local cache is searched first for potential answers. If unsuccessful, the query is forwarded to one or more direct neighbors for answers. This technique leverages node mobility and caching capabilities to avoid the multi-hop communication overhead of directed placement. Using a simplified mobility model, we provide analytical lower and upper bounds on the ability of amorphous placement to achieve uniform field coverage in one and two dimensions. We show that combining informed shuffling of cached samples upon an encounter between two nodes, with the querying of direct neighbors could lead to significant performance improvements. For instance, under realistic mobility models, our simulation experiments show that amorphous placement achieves 10% to 40% better query answering ratio at a 25% to 35% savings in consumed power over directed placement.