Solving the Station Repacking Problem

Fréchette, Alexandre; Newman, Neil; Leyton‐Brown, Kevin

doi:10.1017/9781316471609.039

Cited by 13 publications

(24 citation statements)

References 20 publications

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“…The software searched our gigantic space of candidate algorithm configurations to identify one that worked well on our dataset. ‡ The result of the search was an "algorithm portfolio," dubbed SATFC (for SAT-based feasibility checker), consisting of eight SAT solvers that were constructed to complement each other well when run in parallel and that incorporate several different domain-specific algorithm ideas (19).…”

Section: Market Designmentioning

confidence: 99%

Economics and computer science of a radio spectrum reallocation

Leyton‐Brown

Milgrom

Segal

2017

Proc. Natl. Acad. Sci. U.S.A.

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The recent "incentive auction" of the US Federal Communications Commission was the first auction to reallocate radio frequencies between two different kinds of uses: from broadcast television to wireless Internet access. The design challenge was not just to choose market rules to govern a fixed set of potential trades but also, to determine the broadcasters' property rights, the goods to be exchanged, the quantities to be traded, the computational procedures, and even some of the performance objectives. An essential and unusual challenge was to make the auction simple enough for human participants while still ensuring that the computations would be tractable and capable of delivering nearly efficient outcomes.algorithmic mechanism design | auction theory | incentive auction | market design | dominant strategies Investments in wireless Internet infrastructure are important for US economic growth but have recently been limited by shortages of usable frequencies. With customer reliance on real-time, over the air broadcast television declining steeply, a partial solution is to reassign some television broadcast frequencies. What is the best way to do that? Can a reassignment be reconciled with the license rights of station owners? Dealing with these questions has raised new challenges and brought together researchers in economics and computer science to devise and build an innovative market-based solution.One approach would be to ask the Federal Communications Commission (FCC) to try to compute and implement the optimal reassignment. It would need to decide how many television channels to reallocate to wireless, which stations should stop broadcasting (or be "cleared") to permit this reallocation to occur, which channels to assign to continuing broadcasters, and how to allocate the cleared spectrum among wireless infrastructure companies. In addition, it would need to determine payments: how much compensation to pay to broadcasters for relinquishing their licenses and how much to charge buyers for the new wireless broadband licenses. To carry out these tasks, the agency would need to gather information from television broadcasters, wireless companies, and other affected parties (radio astronomers, users of wireless microphones, etc.), each of whom might make self-serving claims to manipulate the outcome to its advantage. For example, broadcasters could exaggerate the value of broadcast spectrum to promote higher prices, whereas other affected parties might belittle broadcaster values to keep prices low.Given the considerable informational challenges in such planning, it is useful to explore alternatives. Hayek (1) claimed that the beauty of a well-functioning market is that participants, acting only in their own interests and using only their own information, can coordinate effectively and voluntarily to achieve a good aggregate outcome. Classical economic theory develops this idea, assuming that the market is populated by small buyers and sellers, that goods are homogeneous, that buyers and sellers find one another...

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Section: Market Designmentioning

confidence: 99%

Economics and computer science of a radio spectrum reallocation

Leyton‐Brown

Milgrom

Segal

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…To describe the method, we first reformulate equations (18)- (19) by introducing witness binary variables β(x) ∈ {−1, 1} h to enforce the equality constraints (17), that is, P F (x, β(x)|θ) = 0. Thus, we can rewrite Φ(θ) as the SMT problem Φ(θ, β) defined by 11 For vectors a, b, we use a ≡ b as a shorthand for (…”

Section: Improving Efficiency and Scalability Using Variable Eliminationmentioning

confidence: 99%

“…For preprocessing we rely on the ABC tool suite [90]. The same software is capable of performing technology mapping, though a Python version is available in the TECHMAPPING library 17 .…”

Section: Preliminary Experimental Evaluationmentioning

confidence: 99%

Solving SAT and MaxSAT with a Quantum Annealer: Foundations and a Preliminary Report

Bian

Chudak

Macready

et al. 2017

Lecture Notes in Computer Science

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Quantum annealers (QAs) are specialized quantum computers that minimize objective functions over discrete variables by physically exploiting quantum effects. Current QA platforms allow for the optimization of quadratic objectives defined over binary variables (qubits), also known as Ising problems. In the last decade, QA systems as implemented by D-Wave have scaled with Moore-like growth. Current architectures provide 2048 sparsely-connected qubits, and continued exponential growth is anticipated, together with increased connectivity.We explore the feasibility of such architectures for solving SAT and MaxSAT problems as QA systems scale. We develop techniques for effectively encoding SAT -and, with some limitations, MaxSAT-into Ising problems compatible with sparse QA architectures. We provide the theoretical foundations for this mapping, and present encoding techniques that combine offline Satisfiability and Optimization Modulo Theories with on-the-fly placement and routing. Preliminary empirical tests on a current generation 2048-qubit D-Wave system support the feasibility of the approach for certain SAT and MaxSAT problems. 1 Superposition is perhaps the best-known and most surprising aspect of quantum physics (e.g. the famous Scrödinger's cat which is both dead and alive prior to observation).

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“…During the development of SATFC [11] the FCC shared with us a wide range of anonymized problem instances that arose in auction simulations they performed in order to validate the auction design. These formed the "training set" we used in the deep optimization process when constructing SATFC 2.3.1.…”

Section: Data From Auction Simulationsmentioning

confidence: 99%

Deep optimization for spectrum repacking

2017

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Over 13 months in 2016-17 the US Federal Communications Commission conducted an "incentive auction" to repurpose radio spectrum from broadcast television to wireless internet. In the end, the auction yielded $19.8 billion, $10.05 billion of which was paid to 175 broadcasters for voluntarily relinquishing their licenses across 14 UHF channels. Stations that continued broadcasting were assigned potentially new channels to fit as densely as possible into the channels that remained. The government netted more than $7 billion (used to pay down the national debt) after covering costs. A crucial element of the auction design was the construction of a solver, dubbed SATFC, that determined whether sets of stations could be "repacked" in this way; it needed to run every time a station was given a price quote. This paper describes the process by which we built SATFC. We adopted an approach we dub "deep optimization", taking a data-driven, highly parametric, and computationally intensive approach to solver design. More specifically, to build SATFC we designed software that could pair both complete and local-search SAT-encoded feasibility checking with a wide range of domain-specific techniques, such as constraint graph decomposition and novel caching mechanisms that allow for reuse of partial solutions from related, solved problems. We then used automatic algorithm configuration techniques to construct a portfolio of eight complementary algorithms to be run in parallel, aiming to achieve good performance on instances that arose in proprietary auction simulations. To evaluate the impact of our solver in this paper, we built an open-source reverse auction simulator. We found that within the short time budget required in practice, SATFC solved more than 95% of the problems it encountered. Furthermore, the incentive auction paired with SATFC produced nearly optimal allocations in a restricted setting and substantially outperformed other alternatives at national scale.

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Solving the Station Repacking Problem

Cited by 13 publications

References 20 publications

Economics and computer science of a radio spectrum reallocation

Economics and computer science of a radio spectrum reallocation

Solving SAT and MaxSAT with a Quantum Annealer: Foundations and a Preliminary Report

Deep optimization for spectrum repacking

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