Good Worst-case Performance Research Articles

Worst-Case VCG Redistribution Mechanism Design Based on the Lottery Ticket Hypothesis

We study worst-case VCG redistribution mechanism design for the public project problem. The mechanism design task comes down to designing a payment function that maximizes the worst-case allocative efficiency ratio. We use a multilayer perceptron (MLP) with ReLU activation to model the payment function and use mixed integer programming (MIP) to solve for the worst-case type profiles that maximally violate the mechanism design constraints. We collect these worst-case type profiles and use them as training samples to train toward better worst-case mechanisms. In practice, we require a tiny neural network structure for the above approach to scale. The Lottery Ticket Hypothesis states that a large network is likely to contain a "winning ticket" -- a much smaller subnetwork that "won the initialization lottery", which makes its training particularly effective. Motivated by this hypothesis, we train a large network and prune it into a tiny subnetwork. We run MIP-based worst-case training on the drawn subnetwork and evaluate the resulting mechanism's worst-case performance. If the subnetwork does not achieve good worst-case performance, then we record the type profiles that cause the current draw to be bad. To draw again, we restore the large network to its initial weights and prune using recorded type profiles from earlier draws, therefore avoiding drawing the same ticket twice. We expect to eventually encounter a tiny subnetwork that leads to effective training for our worst-case mechanism design task. Lastly, a by-product of multiple ticket draws is an ensemble of mechanisms with different worst cases, which improves the worst-case performance further. Using our approach, we find previously unknown optimal mechanisms for up to 5 agents. Our results confirm the tightness of existing theoretical upper bounds. For up to 20 agents, we derive significantly improved worst-case mechanisms, surpassing a long list of existing manual results.

Average-Case Verification of the Quantum Fourier Transform Enables Worst-Case Phase Estimation

The quantum Fourier transform (QFT) is a key primitive for quantum computing that is typically used as a subroutine within a larger computation, for instance for phase estimation. As such, we may have little control over the state that is input to the QFT. Thus, in implementing a good QFT, we may imagine that it needs to perform well on arbitrary input states. Verifying this worst-case correct behaviour of a QFT-implementation would be exponentially hard (in the number of qubits) in general, raising the concern that this verification would be impossible in practice on any useful-sized system. In this paper we show that, in fact, we only need to have good average-case performance of the QFT to achieve good worst-case performance for key tasks – phase estimation, period finding and amplitude estimation. Further we give a very efficient procedure to verify this required average-case behaviour of the QFT.

Providing Service Continuity in Clouds Under Power Outage

In cloud computing, it is crucial to maintain service continuity, while power outage is one of the most common and serious threats. To improve the resilience of cloud against power outage, a service provider usually deploys emergency energy supply (e.g., UPSs and generators) in a data center. When a power outage at a data center happens, the cloud service provider needs to make the operation decision on which subset of VMs to keep running and which servers to host such VMs to minimize its loss (or maximize its profit) using the emergency energy supply while the selected VMs are running in the affected data center until they are finished, migrated to other data centers, or normal power supply of the affected data center has been restored. No prior research has theoretically studied such a cloud service continuity problem under power outage. In this paper, we tackle this challenge and investigate the cloud service continuity problem. Specifically, we consider that a profit is associated with maintaining the continuity of a service, denoted as service continuity profit. Based on that we first formulate an optimization problem that aims to maximize the total profit subject to energy constrains. After showing the hardness of the problem, we focus on the design of approximation algorithms for solving the problem, where we consider two practical cases. In the first one with sufficient number of servers for re-provisioning, we develop a constant approximation algorithm of which the worst-case performance approaches the optimal solution within a constant factor (≈4.5-6.4). In the second one, we consider the general case with limited number of servers, and we develop an approximation algorithm with an approximation ratio of around 5.7-8. By combining these two algorithms together, we can achieve both good worst-case performance and average performance. Simulation results demonstrate the efficiency in terms of maximizing the service continuity profit of the proposed algorithms.

Partitioning Real-Time Tasks With Replications on Multiprocessor Embedded Systems

Executing computing tasks with replications is an essential choice to achieve fault-tolerance in designing real-time, embedded systems. A problem of maximizing the number of real-time tasks with replications running on a multiprocessor embedded system is discussed in this letter. The partitioning problem can be modeled as a variant of the bin-packing problem. In the original problem, it is known that the first-fit (FF) method has a good worst-case performance bound of 4/3. Whether or not the same bound is achievable in the variant problem remains an open question. This letter closes the question by proving that the worst-case performance bound of using the FF method approaches to 2 but it never reaches it. Then, a tight bound of asymptotic worst-case performance is shown.

FireFly

Conventional static datacenter (DC) network designs offer extreme cost vs. performance tradeoffs---simple leaf-spine networks are cost-effective but oversubscribed, while "fat tree"-like solutions offer good worst-case performance but are expensive. Recent results make a promising case for augmenting an oversubscribed network with reconfigurable inter-rack wireless or optical links. Inspired by the promise of reconfigurability, this paper presents FireFly, an inter-rack network solution that pushes DC network design to the extreme on three key fronts: (1) all links are reconfigurable; (2) all links are wireless; and (3) non top-of-rack switches are eliminated altogether. This vision, if realized, can offer significant benefits in terms of increased flexibility, reduced equipment cost, and minimal cabling complexity. In order to achieve this vision, we need to look beyond traditional RF wireless solutions due to their interference footprint which limits range and data rates. Thus, we make the case for using free-space optics (FSO). We demonstrate the viability of this architecture by (a) building a proof-of-concept prototype of a steerable small form factor FSO device using commodity components and (b) developing practical heuristics to address algorithmic and system-level challenges in network design and management.

Performance Evaluation of Modified Echelon <i>(r, Q)</I> Policies for Stochastic Serial Inventory Systems

We consider the classic continuous-review N-stage serial inventory system with a homogeneous Poisson demand arrival process at the most downstream stage (Stage 1). Any shipment to each stage, regardless of its size, incurs a positive fixed setup cost and takes a positive constant leadtime. The optimal policy for this system under the long-run average cost criterion is unknown. Finding a good worst-case performance guarantee for this problem remains an open problem. We tackle this problem by introducing a class of modified echelon (r, Q) policies that do not require Q_{i 1}/Q_i to be a positive integer: Stage i 1 ships to Stage i based on its observation of the echelon inventory position at Stage i; if it is at or below r_i and Stage i 1 has positive on-hand inventory, then a shipment is sent to Stage i to raise its echelon inventory position to r_i Q_i as close as possible. We construct a heuristic policy within this class of policies, which has the following features: First, it has provably primitive-dependent performance bounds. In a two-stage system, the performance of the heuristic policy is guaranteed to be within (1 K_1/K_2) times of the optimal cost, where K_1 is the downstream fixed cost and K_2 is the upstream fixed cost. We also provide an alternative performance bound, which depends on efficiently-computable optimal (r, Q) solutions to N single-stage systems, but tends to be tighter. Second, the heuristic is simple, efficiently computable and numerically performs well, likely to even outperform the optimal integer-ratio echelon (r,Q) policies when K_1 is dominated by K_2. Third, the heuristic is asymptotically optimal, as we take some dominant relationships, between the setup or holding cost primitives at an upstream stage and its immediate downstream stage, to the extreme, e.g., when h_2/h_1\rightarrow0, where h_1 is the downstream holding cost parameter and h_2 is the upstream holding cost parameter.

Modified Echelon (r, Q) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory Systems

We consider the classic continuous-review Nstage serial inventory system with a homogeneous Poisson demand arrival process at the most downstream stage (Stage 1). Any shipment to each stage, regardless of its size, incurs a positive fixed setup cost and takes a positive constant lead time. The optimal policy for this system under the long-run average cost criterion is unknown. Finding a good worst-case performance guarantee remains an open problem. We tackle this problem by introducing a class of modified echelon (r, Q) policies that do not require Qi + 1/Qi to be a positive integer: Stage i + 1 ships to Stage i based on its observation of the echelon inventory position at Stage i; if it is at or below ri and Stage i + 1 has positive on-hand inventory, then a shipment is sent to Stage i to raise its echelon inventory position to ri + Qi as close as possible. We construct a heuristic policy within this class of policies, which has the following features: First, it has provably primitive-dependent performance bounds. In a two-stage system, the performance of the heuristic policy is guaranteed to be within (1 + K1/K2) times the optimal cost, where K1 is the downstream fixed cost and K2 is the upstream fixed cost. We also provide an alternative performance bound, which depends on efficiently computable optimal (r, Q) solutions to N single-stage systems but tends to be tighter. Second, the heuristic is simple, it is efficiently computable and it performs well numerically; it is even likely to outperform the optimal integer-ratio echelon (r,Q) policies when K1 is dominated by K2. Third, the heuristic is asymptotically optimal when we take some dominant relationships between the setup or holding cost primitives at an upstream stage and its immediate downstream stage to the extreme, for example, when h2/h1 → 0, where h1 is the downstream holding cost parameter and h2 is the upstream holding cost parameter.

Fast parameterized matching with q-grams

Two strings parameterize match if there is a bijection defined on the alphabet that transforms the first string character by character into the second string. The problem of finding all parameterized matches of a pattern in a text has been studied in both one and two dimensions but the research has been centered on developing algorithms with good worst-case performance. We present algorithms that solve this problem in sublinear time on average for moderately repetitive patterns.

The Ordered Open-End Bin-Packing Problem

We study a variant of the classical bin-packing problem, the ordered open-end bin-packing problem, where first a bin can be filled to a level above 1 as long as the removal of the last piece brings the bin's level back to below 1 and second, the last piece is the largest-indexed piece among all pieces in the bin. We conduct both worst-case and average-case analyses for the problem. In the worst-case analysis, pieces of size 1 play distinct roles and render the analysis more difficult with their presence. We give lower bounds for the performance ratio of any online algorithm for cases both with and without the 1-pieces, and in the case without the 1-pieces, identify an online algorithm whose worst-case performance ratio is less than 2 and an offline algorithm with good worst-case performance. In the average-case analysis, assuming that pieces are independently and uniformly drawn from [0, 1], we find the optimal asymptotic average ratio of the number of occupied bins over the number of pieces. We also introduce other online algorithms and conduct simulation study on the average-case performances of all the proposed algorithms.

Constraint satisfaction algorithms for graph pattern matching

Graph pattern matching is a central problem in many application fields. Since it is NP-complete, we cannot expect to find algorithms with a good worst-case performance. However, there is still room for general procedures with a good average performance. In this paper we explore four different solving approaches within the constraint satisfaction framework, and introduce a new algorithm, which we call nRF+. The algorithm is a refinement of really full look ahead that takes advantage of the problem structure in order to enhance the look ahead procedure. We give a formal proof that nRF+ is superior to the other approaches in terms of number of visited nodes. An additional contribution of this paper is the introduction of a new benchmark for testing algorithms in this domain. It is formed by a large set of well-defined graphs of very diverse nature. In this benchmark, we show that nRF+ can efficiently solve a broad range of problems, while still leaving many problem instances unsolved. The use of this challenging benchmark is encouraged for future algorithms evaluation.

Indexing for Data Models with Constraints and Classes

We examine I/O-efficient data structures that provide indexing support for new data models. The database languages of these models include concepts from constraint programming (e.g., relational tuples are generated to conjunctions of constraints) and from object-oriented programming (e.g., objects are organized in class hierarchies). Letnbe the size of the database,cthe number of classes,Bthe page size on secondary storage, andtthe size of the output of a query: (1) Indexing by one attribute in many constraint data models is equivalent to external dynamic interval management, which is a special case of external dynamic two-dimensional range searching. We present a semi-dynamic data structure for this problem that has worst-case spaceO(n/B) pages, query I/O timeO(logBn+t/B) andO(logBn+(logBn)2/B) amortized insert I/O time. Note that, for the static version of this problem, this is the first worst-case optimal solution. (2) Indexing by one attribute and by class name in an object-oriented model, where objects are organized as a forest hierarchy of classes, is also a special case of external dynamic two-dimensional range searching. Based on this observation, we first identify a simple algorithm with good worst-case performance, query I/O timeO(log2clogBn+t/B), update I/O timeO(log2clogBn) and spaceO((n/B)log2c) pages for the class indexing problem. Using the forest structure of the class hierarchy and techniques from the constraint indexing problem, we improve its query I/O time toO(logBn+t/B+log2B).

Hashing and trie algorithms for partial match retrieval

File designs suitable for retrieval from a file of k -letter words when queries may be only partially specified are examined. A new class of partial match file designs (called PMF designs) based upon hash coding and trie search algorithms which provide good worst-case performance is introduced. Upper bounds on the worst-case performance of these designs are given along with examples of files achieving the bound. Other instances of PMF designs are known to have better worst-case performances. The implementation of the file designs with associated retrieval algorithms is considered. The amount of storage required is essentially that required of the records themselves.