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Free energy and complexity of spherical bipartite models
We investigate both free energy and complexity of the spherical bipartite
spin glass model. We first prove a variational formula in high temperature for
the limiting free energy based on the well-known Crisanti-Sommers
representation of the mixed p-spin spherical model. Next, we show that the mean
number of local minima at low levels of energy is exponentially large in the
size of the system and we derive a bound on the location of the ground state
energy.Comment: 22 page
The Energy Complexity of Broadcast
Energy is often the most constrained resource in networks of battery-powered
devices, and as devices become smaller, they spend a larger fraction of their
energy on communication (transceiver usage) not computation. As an imperfect
proxy for true energy usage, we define energy complexity to be the number of
time slots a device transmits/listens; idle time and computation are free.
In this paper we investigate the energy complexity of fundamental
communication primitives such as broadcast in multi-hop radio networks. We
consider models with collision detection (CD) and without (No-CD), as well as
both randomized and deterministic algorithms. Some take-away messages from this
work include:
1. The energy complexity of broadcast in a multi-hop network is intimately
connected to the time complexity of leader election in a single-hop (clique)
network. Many existing lower bounds on time complexity immediately transfer to
energy complexity. For example, in the CD and No-CD models, we need
and energy, respectively.
2. The energy lower bounds above can almost be achieved, given sufficient
() time. In the CD and No-CD models we can solve broadcast using
energy and energy,
respectively.
3. The complexity measures of Energy and Time are in conflict, and it is an
open problem whether both can be minimized simultaneously. We give a tradeoff
showing it is possible to be nearly optimal in both measures simultaneously.
For any constant , broadcast can be solved in
time with
energy, where is the diameter of the network
Energy-Efficient Algorithms
We initiate the systematic study of the energy complexity of algorithms (in
addition to time and space complexity) based on Landauer's Principle in
physics, which gives a lower bound on the amount of energy a system must
dissipate if it destroys information. We propose energy-aware variations of
three standard models of computation: circuit RAM, word RAM, and
transdichotomous RAM. On top of these models, we build familiar high-level
primitives such as control logic, memory allocation, and garbage collection
with zero energy complexity and only constant-factor overheads in space and
time complexity, enabling simple expression of energy-efficient algorithms. We
analyze several classic algorithms in our models and develop low-energy
variations: comparison sort, insertion sort, counting sort, breadth-first
search, Bellman-Ford, Floyd-Warshall, matrix all-pairs shortest paths, AVL
trees, binary heaps, and dynamic arrays. We explore the time/space/energy
trade-off and develop several general techniques for analyzing algorithms and
reducing their energy complexity. These results lay a theoretical foundation
for a new field of semi-reversible computing and provide a new framework for
the investigation of algorithms.Comment: 40 pages, 8 pdf figures, full version of work published in ITCS 201
Energy and Complexity
Sustainable energy systems are complex sociotechnical systems with a social network of many players that ātogetherā develop, operate, and maintain the technical infrastructure. No single player controls the system, but their actions are coordinated through a range of institutionsāinformal and formal rulesāand regulations. As the control is distributed among actors, the overall system behaviour (at different time scales) emerges from operating practices and characteristics, from(dis)investment decisions, and fromother aspects of the playersā strategies
On Complexity, Energy- and Implementation-Efficiency of Channel Decoders
Future wireless communication systems require efficient and flexible baseband
receivers. Meaningful efficiency metrics are key for design space exploration
to quantify the algorithmic and the implementation complexity of a receiver.
Most of the current established efficiency metrics are based on counting
operations, thus neglecting important issues like data and storage complexity.
In this paper we introduce suitable energy and area efficiency metrics which
resolve the afore-mentioned disadvantages. These are decoded information bit
per energy and throughput per area unit. Efficiency metrics are assessed by
various implementations of turbo decoders, LDPC decoders and convolutional
decoders. New exploration methodologies are presented, which permit an
appropriate benchmarking of implementation efficiency, communications
performance, and flexibility trade-offs. These exploration methodologies are
based on efficiency trajectories rather than a single snapshot metric as done
in state-of-the-art approaches.Comment: Submitted to IEEE Transactions on Communication
Complexity vs Energy: Theory of Computation and Theoretical Physics
This paper is a survey dedicated to the analogy between the notions of {\it
complexity} in theoretical computer science and {\it energy} in physics. This
analogy is not metaphorical: I describe three precise mathematical contexts,
suggested recently, in which mathematics related to (un)computability is
inspired by and to a degree reproduces formalisms of statistical physics and
quantum field theory.Comment: 23 pages. Talk at the satellite conference to ECM 2012, "QQQ Algebra,
Geometry, Information", Tallinn, July 9-12, 201
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