21,097 research outputs found
Energy Complexity of Distance Computation in Multi-hop Networks
Energy efficiency is a critical issue for wireless devices operated under
stringent power constraint (e.g., battery). Following prior works, we measure
the energy cost of a device by its transceiver usage, and define the energy
complexity of an algorithm as the maximum number of time slots a device
transmits or listens, over all devices. In a recent paper of Chang et al. (PODC
2018), it was shown that broadcasting in a multi-hop network of unknown
topology can be done in energy. In this paper, we continue
this line of research, and investigate the energy complexity of other
fundamental graph problems in multi-hop networks. Our results are summarized as
follows.
1. To avoid spending energy, the broadcasting protocols of Chang
et al. (PODC 2018) do not send the message along a BFS tree, and it is open
whether BFS could be computed in energy, for sufficiently large . In
this paper we devise an algorithm that attains energy
cost.
2. We show that the framework of the round lower bound proof
for computing diameter in CONGEST of Abboud et al. (DISC 2017) can be adapted
to give an energy lower bound in the wireless network model
(with no message size constraint), and this lower bound applies to -arboricity graphs. From the upper bound side, we show that the energy
complexity of can be attained for bounded-genus graphs
(which includes planar graphs).
3. Our upper bounds for computing diameter can be extended to other graph
problems. We show that exact global minimum cut or approximate -- minimum
cut can be computed in energy for bounded-genus graphs
Optimizing I/O for Big Array Analytics
Big array analytics is becoming indispensable in answering important
scientific and business questions. Most analysis tasks consist of multiple
steps, each making one or multiple passes over the arrays to be analyzed and
generating intermediate results. In the big data setting, I/O optimization is a
key to efficient analytics. In this paper, we develop a framework and
techniques for capturing a broad range of analysis tasks expressible in
nested-loop forms, representing them in a declarative way, and optimizing their
I/O by identifying sharing opportunities. Experiment results show that our
optimizer is capable of finding execution plans that exploit nontrivial I/O
sharing opportunities with significant savings.Comment: VLDB201
Thermodynamic arrow of time of quantum projective measurements
We investigate a thermodynamic arrow associated with quantum projective
measurements in terms of the Jensen-Shannon divergence between the probability
distribution of energy change caused by the measurements and its time reversal
counterpart. Two physical quantities appear to govern the asymptotic values of
the time asymmetry. For an initial equilibrium ensemble prepared at a high
temperature, the energy fluctuations determine the convergence of the time
asymmetry approaching zero. At low temperatures, finite survival probability of
the ground state limits the time asymmetry to be less than . We
illustrate our results for a concrete system and discuss the fixed point of the
time asymmetry in the limit of infinitely repeated projections.Comment: 6 pages in two columns, 1 figure, to appear in EP
A Time Hierarchy Theorem for the LOCAL Model
The celebrated Time Hierarchy Theorem for Turing machines states, informally,
that more problems can be solved given more time. The extent to which a time
hierarchy-type theorem holds in the distributed LOCAL model has been open for
many years. It is consistent with previous results that all natural problems in
the LOCAL model can be classified according to a small constant number of
complexities, such as , etc.
In this paper we establish the first time hierarchy theorem for the LOCAL
model and prove that several gaps exist in the LOCAL time hierarchy.
1. We define an infinite set of simple coloring problems called Hierarchical
-Coloring}. A correctly colored graph can be confirmed by simply
checking the neighborhood of each vertex, so this problem fits into the class
of locally checkable labeling (LCL) problems. However, the complexity of the
-level Hierarchical -Coloring problem is ,
for . The upper and lower bounds hold for both general graphs
and trees, and for both randomized and deterministic algorithms.
2. Consider any LCL problem on bounded degree trees. We prove an
automatic-speedup theorem that states that any randomized -time
algorithm solving the LCL can be transformed into a deterministic -time algorithm. Together with a previous result, this establishes that on
trees, there are no natural deterministic complexities in the ranges
--- or ---.
3. We expose a gap in the randomized time hierarchy on general graphs. Any
randomized algorithm that solves an LCL problem in sublogarithmic time can be
sped up to run in time, which is the complexity of the distributed
Lovasz local lemma problem, currently known to be and
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