Bits Of Advice Research Articles

Online computation with untrusted advice

We study a generalization of the advice complexity model of online computation in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms that are robust if the advice is adversarial, and efficient is the advice is foolproof. We focus on four well-studied online problems, namely ski rental, online bidding, bin packing and list update. For ski rental and online bidding, we show how to obtain algorithms that are Pareto-optimal with respect to the competitive ratios achieved, whereas for bin packing and list update, we give online algorithms with worst-case tradeoffs in their competitiveness, depending on whether the advice is trusted or adversarial. More importantly, we demonstrate how to prove lower bounds, within this model, on the tradeoff between the number of advice bits and the competitiveness of any online algorithm.

Advice complexity of adaptive priority algorithms

The priority model was introduced to capture “greedy-like” algorithms. Motivated by the success of advice complexity in the area of online algorithms, the fixed priority model was extended to include advice, and a reduction-based framework was developed for proving lower bounds on the amount of advice required to achieve certain approximation ratios in this rather powerful model. To capture most of the algorithms that are considered greedy-like, the even stronger model of adaptive priority algorithms is needed. We extend the adaptive priority model to include advice. We modify the reduction-based framework from the fixed priority case to work with the more powerful adaptive priority algorithms, simplifying the proof of correctness and strengthening all previous lower bounds by a factor of two in the process.As evidence that adding advice to adaptive priority algorithms extends both adaptive priority algorithms and online algorithms with advice, we present a purely combinatorial adaptive priority algorithm with advice for Minimum Vertex Cover on triangle-free graphs of maximum degree three. Our algorithm achieves optimality and uses at most 7n/22 bits of advice. No adaptive priority algorithm without advice can achieve optimality without advice, and we prove that an online algorithm with advice needs more than 7n/22 bits of advice to reach optimality.We show connections between exact algorithms and priority algorithms with advice. The branching in branch-and-reduce algorithms can be seen as trying all possible advice strings, and all priority algorithms with advice that achieve optimality define corresponding exact algorithms, priority exact algorithms. Lower bounds on advice-based adaptive algorithms imply lower bounds on running times of exact algorithms designed in this way.

We need to talk

We need to talk

Editors' Page

Editors' Page Stephanie G'schwind and Donald Revell Whatever plans you think you got, you better get some others." An ominous bit of advice given, in Brendan McKennedy's "Deep River," to a young woman struggling to make a meaningful life as a millhand in 1920s North Carolina, it might well be the motto for the last three years, when we've had to pivot, accommodate, reimagine, reconfigure. It certainly rings true for the characters in this issue's fiction, who find themselves having to make all manner of unforeseen adjustments. In Joanna Pearson's "The Favor," a couple become the hosts to an unexpected houseguest at a time when they are questioning the boundaries of what makes a family. The narrator of Deepa Varadarajan's "How to Give a Best Man Toast" wrestles with the shifting of attachments as his beloved older brother gets married. And in Naihobe Gonzalez's "Southern Cemetery," a young woman spontaneously spends an evening with a new friend, exploring the risky space between safety and uncertainty, confronting her relationship to fear. Shifting focus, the essays here are concerned with the spaces we inhabit—and how they shape us. "First you live in a house, and then it lives in you," writes Emily Winakur in "Who Lives in That House," an essay that explores, among other things, the relationship of place to memory. Jonathan Gleason's braided essay "Proxemics" is a meditation on architecture, spatial relationships, family, penitence, and forgiveness. And in "The Other Erica," Erica Goss contemplates the multigenerational impact of her grandmother's death, leading her to search for the house in Germany where her mother and grandmother endured the Second World War, seeking clues about her mother's, grandmother's, and, ultimately, her own identity. Whatever space you find yourself in, whatever plans you have, I hope you can make room and time for the stories, essays, and poems we've gathered for you in these pages. Welcome to the spring issue. [End Page 1] ________ Given the turbulent mundanity of our day—its diminished expectations and dire prospects—it is time, surely, to take a lesson from springtime itself and to venture all upon a reckless moment of beauty. When it comes to beauty, I'm with Cocteau: "a little too much is just enough for me." Call it, as Emma De Lisle does, "some helpless faith of my flesh," but I cannot help but choose the apple blossom over the killing frost, the bear cub over the melting ice cap, no matter what the odds. The question, then, becomes just how and when to improve those odds in beauty's favor. Our poets rise amply to the question. Wisely, Rachel Abramowitz advises, "If you see a saint, speak to it," i.e., engage with transcendence wherever it appears, then ask for directions. Angela Ball suggests, with just the right touch of metaphysical insouciance, that we explore "the space between / two swans," there, perhaps, to discover the grace that moves all graciousness. It's worth a try, and in the trying we may delight to find what James Davis May calls (and calls for) "not just beauty, then, but its excess." When I was young, the phrase "too much" was an earnest form of praise. In our more-than-praiseworthy gathering of poets, may you find ample and adequate excess. [End Page 2] Copyright © 2023 Center for Literary Publishing

Balut

Balut Jinny Koh (bio) Angela Flores was twenty when she started work at the Ong’s bungalow, although her work permit said she was twenty-three, the legal age for domestic helpers in Singapore. Her supervisor at the agency had assured her it was just a minor detail, that everyone did that, and as long as the Ongs did not find out, it was okay to lie. “Trust me. Just keep quiet and you’ll be fine,” Mrs Lim said as she handed the contract to Angela. Even under the dull fluorescent light, Mrs Lim’s diamond ring, the size of a chickpea, glittered at all angles. Angela had never seen such a big diamond before, and its price and authenticity were frequent topics of speculation among the domestic helpers in the office. After all, there wasn’t much to do while waiting to be employed. “You want to work here, right?” Mrs Lim went on. “If not, you can go back to the Philippines, you know.” She paused and lifted a brow. “But don’t forget, your air ticket to come here cost money, money which you haven’t paid off.” Angela didn’t want—or rather, couldn’t afford—to go home. Her family depended on her for rent and meals. So she swallowed her doubts, signed the contract, and took a seat with the other women in the small, windowless office at the Bukit Timah Shopping Centre. They were dressed in jeans and the same yellow polo shirt with the company’s logo—Star Maid—emblazoned on the front pocket. Facing a glass panel, they formed one straight row so that any potential employers walking past could get a good look. Most of them, including Angela, kept their hair short with their fringe pinned to the side, while the few sporting long black hair wore them in a tight ponytail. Competition was stiff in this building, where every other unit held a maid agency, so Mrs Lim was particularly strict with their appearance and decorum. No untucked shirts. No snacking. And, most important of all, no sad, dour faces. “No one wants an unhappy maid,” Mrs Lim would say. “They want Star Maids!” With Angela were women of varying ages, some much older, from the Philippines, Indonesia, and Myanmar. Many of them had worked at other homes before a dispute with their employers brought them back to this cramped office. They congratulated Angela on her first job and murmured words of encouragement. Time will pass quickly when you are busy. Don’t call home too often or your boss won’t be happy. And remember, don’t argue. Angela nodded and took in every bit of advice. She knew she needed to “behave well” in order to maintain a good relationship with her bosses. She had heard enough horror stories about employers who abused their domestic helpers—withholding their salaries, hitting them with metal [End Page 40] spatulas and bamboo poles, starving them—and could only pray that the Ongs were going to be kind and gracious. ________ Every day, Angela cleaned the Ong’s three-storey bungalow, washed and ironed their clothes, cooked three meals (four, if Mr Ong worked late), and fed their Jack Russell, Rocky. Even though she had no prior work experience, the Ongs were willing to “try her out” because Mrs Lim had vouched for her character. They had requested for a simple and honest domestic helper, one who was not capable of cheating, finding a boyfriend, or mistreating their son. On the first day of work, Mrs Ong had pulled Angela aside and warned her not to take anything from the house without permission. Not a slice of fish from the fridge or a crumb of biscuit from the pantry. “You want anything, just ask. Don’t steal.” Angela had never stolen anything in her life and was miffed by the woman’s attitude. But she simply said, “Yes, ma’am, I will not take.” Now, Mrs Ong was glaring at her over the dinner table. She was beautiful. Glamorous, actually. Her dyed chestnut hair fell in loose curls down her shoulders, and her skin was fair and smooth, the product...

Exploring sparse graphs with advice

Graph exploration is a theoretical model of the crucial task of moving an agent through an unknown environment. Here, an algorithm has to guide an explorer through a network with n vertices and m edges, visiting every vertex at least once. We consider the fixed-graph scenario by Kalyanasundaram and Pruhs (ICALP, 1993), where the explorer sees all vertices reachable in one step, their unique names and their distance from the current position.The algorithm only learns the structure of the graph during computation. Therefore, we are interested in the amount of crucial a-priori information (the advice complexity) needed to solve the problem optimally.We look at graph exploration on directed graphs and focus on cyclic solutions. It is known that O(nlog⁡n) bits of advice are necessary and sufficient to compute an optimal solution for general graphs. We present algorithms with O(m) advice, thus improving the bound for sparse graphs.

Nonuniform Reductions and NP-Completeness

Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger complexity classes. We study the power of nonuniform reductions for NP-completeness, obtaining both separations and upper bounds for nonuniform completeness vs uniform complessness in NP. Under various hypotheses, we obtain the following separations: 1. There is a set complete for NP under nonuniform many-one reductions, but not under uniform many-one reductions. This is true even with a single bit of nonuniform advice. 2. There is a set complete for NP under nonuniform many-one reductions with polynomial-size advice, but not under uniform Turing reductions. That is, polynomial nonuniformity cannot be replaced by a polynomial number of queries. 3. For any fixed polynomial p(n), there is a set complete for NP under uniform 2-truth-table reductions, but not under nonuniform many-one reductions that use p(n) advice. That is, giving a uniform reduction a second query makes it impossible to simulate by a nonuniform reduction with fixed polynomial advice. 4. There is a set complete for NP under nonuniform many-one reductions with polynomial advice, but not under nonuniform many-one reductions with logarithmic advice. This hierarchy theorem also holds for other reducibilities, such as truth-table and Turing. We also consider uniform upper bounds on nonuniform completeness. Hirahara (2015) showed that unconditionally every set that is complete for NP under nonuniform truth-table reductions that use logarithmic advice is also uniformly Turing-complete. We show that under a derandomization hypothesis, every set that is complete for NP under nonuniform truth-table reductions is also uniformly truth-table complete.

Online Algorithms with Advice for the k-search Problem

In the online search problem, a seller seeks to find the maximum price from a sequence of prices 𝒑1, 𝒑2 ,..., 𝒑𝒏 that is revealed in a piece-wise manner. The bound for all prices is well known in advance with 𝒎 � 𝒑𝒊 � 𝑴. In the online 𝒌-search problem, the seller seeks to find the 𝒌 maximum out of the 𝒏 prices. In this paper, we present a tight bound of loglog22(�(���)) on the advice complexity of optimal online algorithms for online 𝒌-search. We also provide online algorithms with advice that use less than the required number of bits and compute the performance guarantee. Although it is natural to expect improvement due to the additional power of advice, we are interested to identify the relationship of additional information with respect to the improvement. We show that with 1 bit of advice, we can already surpass the quality of the best possible deterministic algorithm for online 2-search. We also provide a set of online algorithms, ALG𝒊, that utilizes loglog22(�(�𝑖𝑖 )) advice bits with a competitive ratio of 𝑖𝑀+�⁻� ⁺ ¹ (𝑘 − 𝑖)⁽�⁻� ⁾𝑚) 𝑘 𝑀 . We show that increasing the amount of advice improves the solution quality of the algorithm. Moreover, we compare the power of advice and randomization. We show that for some identified minimum number of advice bits, the lower bound on the competitive ratio of online algorithms with advice is better than any deterministic and randomized algorithm for online 𝒌-search.

Call admission problems on trees

We are given nodes in a communication network that request connections to other nodes. A central authority may accept or reject such a request right away, and once a connection is established its duration is unbounded and its edges cannot be used for other connections; actions are performed without knowledge of future requests, that is, we consider an online setting. We examine this so-called call admission problem in tree networks. The focus is on the quality of solutions achievable in an advice setting, that is, when the central authority has a certain amount of information on the incoming requests.We show that O(mlog2⁡d) bits of additional information are sufficient for an online algorithm run by the central authority to perform as well as an optimal offline algorithm, where m is the number of edges and d is the largest degree in the tree network. In the case of a star tree network, we show that Ω(mlog2⁡d) bits are also necessary (note that d=m). We also present a lower bound on the advice complexity for small constant competitive ratios and an algorithm whose competitive ratio gradually improves with added advice bits to 2⌈log2⁡n⌉, where n is the number of nodes in the network.

Call admission problems on grids with advice

We analyze the online call admission problem on grids, thus generalizing previous results for the path graph. Here the goal is to admit as many communication requests between pairs of computers in a given grid network as possible. The requests arrive in an online fashion, and ask to establish permanent edge-disjoint connections. We are particularly interested in examining how much information about future requests a central authority needs in order to compute an optimal solution or a solution of some given quality; we quantify this information by studying the advice complexity of the problem.Our results show that, without additional information, the central authority cannot perform satisfactorily well, and we establish a lower bound linear in |E| for the number of advice bits needed for near-optimal solutions, where |E| denotes the number of edges in the grid. Furthermore, concerning optimality, we are able to prove nearly tight bounds of at least 0.94|E| and at most 3|E| advice bits. In addition, we state another upper bound in the number of requests k and the number of vertices |V| in the grid of ⌈log2⁡5⋅k+log2⁡3⋅|V|⌉+⌈2log2⁡k⌉ advice bits, which is stronger for a small number of requests.

Two-way and one-way quantum and classical automata with advice for online minimization problems

We consider online algorithms. Typically, the model is investigated with respect to the competitive ratio. In this paper, we explore two-way automata and one-way automata as models for online algorithms. We focus on quantum and classical online algorithms. We show that there are problems that can be solved more efficiently by two-way automata with quantum and classical states than by classical two-way automata in the case of sublogarithmic memory (sublinear size), even if classical automata get advice bits. Additionally, we show that there are problems that can be solved more efficiently by one-way quantum automata than by classical one-way automata in the case of sublogarithmic memory (resp., sublinear size) and in the case of logarithmic memory (resp., linear size) even if classical automata get advice bits.

Postface

Postface

It\u2019s a small bit of advice, but actually on the day, made such a difference\u2026: perceptions of quality in abortion care in England and Wales

BackgroundQuality of care (QOC) is increasingly identified as an important contributor to healthcare outcomes, however little agreement exists on what constitutes quality in abortion care or the recommended indicators from the service-user perspective. Our study aimed to explore perceptions and experiences of abortion QOC in England and Wales.MethodsWe performed in-depth interviews (via phone or in-person) with participants who had an abortion at a nationwide independent sector provider in the previous 6 months. We explored their experiences of the abortion service at each point in the care pathway, their perspectives on what contributed to and detracted from the experience meeting their definitions of quality, and their reflections on different aspects of QOC. We used content analysis to generate themes.ResultsFrom December 2018 to July 2019, we conducted 24 interviews. Ten participants had a surgical and 14 had a medical abortion. Seventeen (71%) were treated in the first 12 weeks of pregnancy and 7 (29%) beyond that, with an average gestational age of 10 weeks + 5 days (range 5–23 + 6). We identified 4 major themes that contributed to participant’s perception of high quality care: (1) interpersonal interactions with staff or other patients, (2) being informed and prepared, (3) participation and choices in care and (4) accessibility. Nearly all participants identified interpersonal interactions with staff as an important contributor to quality with positive interactions often cited as the best part of their abortion experience and negative interactions as the worst. For information and preparation, participant described not only the importance of being well prepared, but how incongruencies between information and the actual experience detracted from quality. Participants said that making choices about their care, for example, method of abortion, was a positive contributor. Finally, participants identified access to care, specifically in relation to waiting times and travel, as an important aspect of QOC.ConclusionsParticipants situated quality in abortion care in 4 domains: interpersonal aspects of care, information and preparation, choices, and accessibility. Indicators identified can be used to develop standard metrics to ensure care meets service-user needs.

Critical Analysis on the Women Employees Work-life Balance during Covid-19 Pandemic in the Airline Industry in Sultanate of Oman.

It has always been a difficult challenge to achieve a satisfactory work-life balance for everyone working in different industries. Still, it is a lot difficult to maintain, especially for women. The purpose of this paper is to find out the problems encountered by women employees of the Airline Industry in Sultanate of Oman to keep up the work-life balance during pandemic while upholding their physical and mental health status at best. This study intends to perceive how the women employees of the Airline Industry in the Sultanate of Oman maintained the work from home because it is not easy to do the house chores and office work at the same time (Moosa, 2017). The existing problems because of the pandemic pushed women employees' mental and physical health at the edge. However, pandemics also open a new gate for women employees to go beyond their limitations and to fight and compete in such situations. The paper has also covered some restrictions about the study with a detailed discussion on the background, scope, and significance of deconstruction. The ongoing research is also about seeking out some solutions for women employees to balance work and life. Further, the paper also includes a few bits of advice for the Airline Industry in the Sultanate of Oman that what steps it should take to make life easy for women employees to attain work-life balance.

Michael Thompson, MD

Michael Thompson, MD

On the advice complexity of the online dominating set problem

A dominating set S of a graph is a set of vertices such that each vertex is in S or has a neighbor in S. The goal of the dominating set problem is to find such a set of minimum cardinality. In the online setting, the graph is revealed vertex by vertex, together with edges to all previously revealed vertices.Advice complexity is a framework to measure the amount of information an online algorithm is lacking. Here, an online algorithm reads advice bits from an infinite binary tape prepared beforehand by an all-knowing oracle. The advice complexity is the total number of advice bits read during the computation. Besides giving some insight into what makes an online problem hard, advice complexity can also be used as a means for proving lower bounds on the competitive ratio achievable by randomized online algorithms.We analyze the advice complexity of the online dominating set problem. For general graphs, we show tight upper and lower bounds for optimality. Then, we use a result for c-competitiveness to prove that no randomized online algorithm can be better than n1−ε-competitive, for any ε>0. Finally, we analyze the advice complexity of various graph classes for optimality.

An asthma plan

An asthma plan

Quantificational Attitudes

The literature contains a popular argument in favor of the position that conditional attitudes (especially intentions and desires) are not simple attitudes with conditional contents but, rather, have a more complex structure. In this paper I show that an analogous argument applies to what we might call quantificational attitudes—like an intention to follow every bit of good advice I receive or a desire to get rabies shots for each bite I incur from an infected bat. The conditions under which these attitudes are satisfied and thwarted are not captured by claiming that they are simple attitudes with quantificational contents. So, the argument supports a novel position—that quantificational attitudes have a more complex structure. After sketching the form of this extra structure, I show how similar considerations count in favor of the existence of genuinely quantificational speech acts.

The Busy Beaver Frontier

The Busy Beaver function, with its incomprehensibly rapid growth, has captivated generations of computer scientists, mathematicians, and hobbyists. In this survey, I o er a personal view of the BB function 58 years after its introduction, emphasizing lesser-known insights, recent progress, and especially favorite open problems. Examples of such problems include: when does the BB function rst exceed the Ackermann function? Is the value of BB(20) independent of set theory? Can we prove that BB(n + 1) > 2BB(n) for large enough n? Given BB(n), how many advice bits are needed to compute BB(n + 1)? Do all Busy Beavers halt on all inputs, not just the 0 input? Is it decidable, given n, whether BB(n) is even or odd?

You Are Invited to a Masked Ball P.S.: Do Not Wear a Mask

You Are Invited to a Masked Ball P.S.:Do Not Wear a Mask David Caldwell (bio) Rob Reiner's 1987 movie The Princess Bride tells the story of a princess, memorably named Buttercup, who is kidnaped and rescued. Fans of the film will recall that Princess Buttercup's abductors are a lovably inept trio of villains, and that her savior in dogged pursuit of the band is a mysterious man in black. His outfit includes a black mask. Genuinely curious, one of the kidnapers, a giant named Fezzik, asks his pursuer, "Why are you wearing a mask? Were you burned with acid, or something like that?" The man in black replies, "Oh no, it's just that they're terribly comfortable. I think everyone will be wearing them in the future." More than thirty years later, the prophetic nature of that whimsical dialogue enhances enjoyment of it, though many would claim it was a bit off in its assessment of comfort level. However, the prediction of universal face coverage resonates no less during the Covid-19 pandemic than does a bit of advice that Fezzik gives his fellow accomplice Inigo Montoya elsewhere in the film. As Montoya prepares to engage their pursuer in a sword fight, he tells his friend. "You be careful. People in masks cannot be trusted." In addition to the role of the mask in various health practices over time, representations in popular culture, theater, literary prose, and eventually in film provide a revealing account of human masking and unmasking over the centuries. America's tumult of mistrust and apprehension over pandemic face coverings in 2020 has unfolded as the latest chapter in the history of humans alternately covering their faces and leaving them unmasked. In particular, a selective examination of masking in other times, both in historical context and in the virtual venues of literature, reveals much about American society since the election of Donald Trump. In The Princess Bride the man in black, played by Cary Elwes, makes his way up the Cliffs of Insanity, through the Fire Swamp, [End Page 199] and into the Pit of Despair--fantasy destinations that again scream metaphorical comparisons to 2020. This tour, however, first provides historical context, then drops in on a couple of exceptionally garish masked balls from 19th and 20th century literature. They are the type of festivity that would be inconceivable for a non-literary party planner. Similarly, prior to the ascendancy of Donald Trump in politics, the unprecedented spectacle of his administration could scarcely have been conceived outside of fantasy. While the Pit of Despair is not a destination on this overview of mask culture, we will drop by 1600 Pennsylvania Avenue. Masks are optional there. Humans have always found reasons to cover their faces, whether as a means of expression or as a tool for concealment. Even the use of masks as protective equipment by various professions in the technological age has historical precedence. Beginning in the 17th century, European plague doctors wore beaked visors with glass eye coverings to protect themselves from miasma, the putrid and supposedly infectious air that was believed to cause the disease. In some European cities and towns, including many where a memorial plague column dominates the public square, historical epidemics remain a part of the cultural fabric. For example in Venice today, replicas of the plague mask are sold as curiosities. Medieval Venice is a particularly instructive example of pandemic response, due to its development of the forty-day quarantine for incoming ships and their crews on two outlying islands, a prerequisite for permission to disembark in the harbor. The word quarantine derives from the Italian term for forty days, quaranta giorni. Between plagues, Venice´s embrace of mask-wearing has historically found a less macabre outlet in costume balls that highlight what is called "cosplay" today. During Carnival season in particular, elaborately decorative face coverings are a staple of Venetian galas. The social convention of the masked ball emerged during the Middle Ages, around the same time as the first epidemics. Though the two phenomena are not necessarily related, their separate deployment of masks is enlightening. After the emergence of the plague...