9,986 research outputs found
Memory lower bounds for deterministic self-stabilization
In the context of self-stabilization, a \emph{silent} algorithm guarantees
that the register of every node does not change once the algorithm has
stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that,
for finding the centers of a graph, for electing a leader, or for constructing
a spanning tree, every silent algorithm must use a memory of
bits per register in -node networks. Similarly, Korman et al. [Dist. Comp.
'07] proved, using the notion of proof-labeling-scheme, that, for constructing
a minimum-weight spanning trees (MST), every silent algorithm must use a memory
of bits per register. It follows that requiring the algorithm
to be silent has a cost in terms of memory space, while, in the context of
self-stabilization, where every node constantly checks the states of its
neighbors, the silence property can be of limited practical interest. In fact,
it is known that relaxing this requirement results in algorithms with smaller
space-complexity.
In this paper, we are aiming at measuring how much gain in terms of memory
can be expected by using arbitrary self-stabilizing algorithms, not necessarily
silent. To our knowledge, the only known lower bound on the memory requirement
for general algorithms, also established at the end of the 90's, is due to
Beauquier et al.~[PODC '99] who proved that registers of constant size are not
sufficient for leader election algorithms. We improve this result by
establishing a tight lower bound of bits per
register for self-stabilizing algorithms solving -coloring or
constructing a spanning tree in networks of maximum degree~. The lower
bound bits per register also holds for leader election
Virtual cluster scheduling through the scheduling graph
This paper presents an instruction scheduling and cluster assignment approach for clustered processors. The proposed technique makes use of a novel representation named the scheduling graph which describes all possible schedules. A powerful deduction process is applied to this graph, reducing at each step the set of possible schedules. In contrast to traditional list scheduling techniques, the proposed scheme tries to establish relations among instructions rather than assigning each instruction to a particular cycle. The main advantage is that wrong or poor schedules can be anticipated and discarded earlier. In addition, cluster assignment of instructions is performed using another novel concept called virtual clusters, which define sets of instructions that must execute in the same cluster. These clusters are managed during the deduction process to identify incompatibilities among instructions. The mapping of virtual to physical clusters is postponed until the scheduling of the instructions has finalized. The advantages this novel approach features include: (1) accurate scheduling information when assigning, and, (2) accurate information of the cluster assignment constraints imposed by scheduling decisions. We have implemented and evaluated the proposed scheme with superblocks extracted from Speclnt95 and MediaBench. The results show that this approach produces better schedules than the previous state-of-the-art. Speed-ups are up to 15%, with average speed-ups ranging from 2.5% (2-Clusters) to 9.5% (4-Clusters).Peer ReviewedPostprint (published version
Entanglement-assisted zero-error source-channel coding
We study the use of quantum entanglement in the zero-error source-channel
coding problem. Here, Alice and Bob are connected by a noisy classical one-way
channel, and are given correlated inputs from a random source. Their goal is
for Bob to learn Alice's input while using the channel as little as possible.
In the zero-error regime, the optimal rates of source codes and channel codes
are given by graph parameters known as the Witsenhausen rate and Shannon
capacity, respectively. The Lov\'asz theta number, a graph parameter defined by
a semidefinite program, gives the best efficiently-computable upper bound on
the Shannon capacity and it also upper bounds its entanglement-assisted
counterpart. At the same time it was recently shown that the Shannon capacity
can be increased if Alice and Bob may use entanglement.
Here we partially extend these results to the source-coding problem and to
the more general source-channel coding problem. We prove a lower bound on the
rate of entanglement-assisted source-codes in terms Szegedy's number (a
strengthening of the theta number). This result implies that the theta number
lower bounds the entangled variant of the Witsenhausen rate. We also show that
entanglement can allow for an unbounded improvement of the asymptotic rate of
both classical source codes and classical source-channel codes. Our separation
results use low-degree polynomials due to Barrington, Beigel and Rudich,
Hadamard matrices due to Xia and Liu and a new application of remote state
preparation.Comment: Title has been changed. Previous title was 'Zero-error source-channel
coding with entanglement'. Corrected an error in Lemma 1.
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
The next few years will be exciting as prototype universal quantum processors
emerge, enabling implementation of a wider variety of algorithms. Of particular
interest are quantum heuristics, which require experimentation on quantum
hardware for their evaluation, and which have the potential to significantly
expand the breadth of quantum computing applications. A leading candidate is
Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates
between applying a cost-function-based Hamiltonian and a mixing Hamiltonian.
Here, we extend this framework to allow alternation between more general
families of operators. The essence of this extension, the Quantum Alternating
Operator Ansatz, is the consideration of general parametrized families of
unitaries rather than only those corresponding to the time-evolution under a
fixed local Hamiltonian for a time specified by the parameter. This ansatz
supports the representation of a larger, and potentially more useful, set of
states than the original formulation, with potential long-term impact on a
broad array of application areas. For cases that call for mixing only within a
desired subspace, refocusing on unitaries rather than Hamiltonians enables more
efficiently implementable mixers than was possible in the original framework.
Such mixers are particularly useful for optimization problems with hard
constraints that must always be satisfied, defining a feasible subspace, and
soft constraints whose violation we wish to minimize. More efficient
implementation enables earlier experimental exploration of an alternating
operator approach to a wide variety of approximate optimization, exact
optimization, and sampling problems. Here, we introduce the Quantum Alternating
Operator Ansatz, lay out design criteria for mixing operators, detail mappings
for eight problems, and provide brief descriptions of mappings for diverse
problems.Comment: 51 pages, 2 figures. Revised to match journal pape
Performance of distributed mechanisms for flow admission in wireless adhoc networks
Given a wireless network where some pairs of communication links interfere
with each other, we study sufficient conditions for determining whether a given
set of minimum bandwidth quality-of-service (QoS) requirements can be
satisfied. We are especially interested in algorithms which have low
communication overhead and low processing complexity. The interference in the
network is modeled using a conflict graph whose vertices correspond to the
communication links in the network. Two links are adjacent in this graph if and
only if they interfere with each other due to being in the same vicinity and
hence cannot be simultaneously active. The problem of scheduling the
transmission of the various links is then essentially a fractional, weighted
vertex coloring problem, for which upper bounds on the fractional chromatic
number are sought using only localized information. We recall some distributed
algorithms for this problem, and then assess their worst-case performance. Our
results on this fundamental problem imply that for some well known classes of
networks and interference models, the performance of these distributed
algorithms is within a bounded factor away from that of an optimal, centralized
algorithm. The performance bounds are simple expressions in terms of graph
invariants. It is seen that the induced star number of a network plays an
important role in the design and performance of such networks.Comment: 21 pages, submitted. Journal version of arXiv:0906.378
A Coloring Algorithm for Disambiguating Graph and Map Drawings
Drawings of non-planar graphs always result in edge crossings. When there are
many edges crossing at small angles, it is often difficult to follow these
edges, because of the multiple visual paths resulted from the crossings that
slow down eye movements. In this paper we propose an algorithm that
disambiguates the edges with automatic selection of distinctive colors. Our
proposed algorithm computes a near optimal color assignment of a dual collision
graph, using a novel branch-and-bound procedure applied to a space
decomposition of the color gamut. We give examples demonstrating the
effectiveness of this approach in clarifying drawings of real world graphs and
maps
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