OpenRaiser/Intern-Atlas huggingface dataset:
Reaping the Benefits of Bundling under High Production Costs
Venue: arXiv cs.GT 2021
Year: 2021

It is well-known that selling different goods in a single bundle can significantly increase revenue. However, bundling is no longer profitable if the goods have high production costs. To overcome this challenge, we introduce a new mechanism, Pure Bundling with Disposal for Cost (PBDC), where after buying the bundle, the customer is allowed to return any subset of goods for their costs. We provide two types of guarantees on the profit of PBDC mechanisms relative to the optimum in the presence of production costs, under the assumption that customers have valuations which are additive over the items and drawn independently. We first provide a distribution-dependent guarantee which shows that PBDC earns at least 1-6c^{2/3} of the optimal profit, where c denotes the coefficient of variation of the welfare random variable. c approaches 0 if there are a large number of items whose individual valuations have bounded coefficients of variation, and our constants improve upon those from the classical result of Bakos and Brynjolfsson (1999) without costs. We then provide a distribution-free guarantee which shows that either PBDC or individual sales earns at least 1/5.2 times the optimal profit, generalizing and improving the constant of 1/6 from the celebrated result of Babaioff et al. (2014). Conversely, we also provide the best-known upper bound on the performance of any partitioning mechanism (which captures both individual sales and pure bundling), of 1/1.19 times the optimal profit, improving on the previously-known upper bound of 1/1.08. Finally, we conduct simulations under the same playing field as the extensive numerical study of Chu et al. (2011), which confirm that PBDC outperforms other simple pricing schemes overall.
Asynchronous Exclusive Selection
Venue: arXiv cs.DC 2021
Year: 2021

We consider the task of assigning unique integers to a group of processes in an asynchronous distributed system of a total of $n$ processes prone to crashes that communicate through shared read-write registers. In the Renaming problem, an arbitrary group of $k\le n$ processes that hold the original names from a range $[N]=\{1,\ldots,N\}$, contend to acquire unique integers in a smaller range $[M]$ as new names using some $r$ auxiliary shared registers. We give number of wait-free renaming algorithms, in particular an adaptive one having $M=8k-\lg k-1$ as a bound on the range of new names that operates in $O(k)$ local steps and uses $r=O(n^2)$ registers. As a lower bound, we show that a wait-free solution to Renaming requires $1+\min\{k-2,\lfloor\log_{2r} \frac{N}{M+k-1}\rfloor\}$ steps in the worst case. We apply renaming algorithms to obtain solutions to Store&Collect problem, which is about a group of $k\le n$ processes with the original names in a range $[N]$ proposing individual values (operation Store) and returning a view of all proposed values (operation Collect), while using some $r$ auxiliary shared read-write registers. We consider a problem Mining-Names, in which processes may repeatedly request positive integers as new names subject to the constraints that no integer can be assigned to different processes and the number of integers never acquired as names is finite in an infinite execution. We give two solutions to Mining-Names in a distributed system in which there are infinitely many shared read-write registers available. A non-blocking solution leaves at most $2n-2$ nonnegative integers never assigned as names, and a wait-free algorithm leaves at most $(n+2)(n-1)$ nonnegative integers never assigned as names.
A Critical Connectivity Radius for Segmenting Randomly-Generated, High Dimensional Data Points
Venue: arXiv cs.LG 2021
Year: 2021

Motivated by a $2$-dimensional (unsupervised) image segmentation task whereby local regions of pixels are clustered via edge detection methods, a more general probabilistic mathematical framework is devised. Critical thresholds are calculated that indicate strong correlation between randomly-generated, high dimensional data points that have been projected into structures in a partition of a bounded, $2$-dimensional area, of which, an image is a special case. A neighbor concept for structures in the partition is defined and a critical radius is uncovered. Measured from a central structure in localized regions of the partition, the radius indicates strong, long and short range correlation in the count of occupied structures. The size of a short interval of radii is estimated upon which the transition from short-to-long range correlation is virtually assured, which defines a demarcation of when an image ceases to be "interesting".
A Coinductive Approach to Proof Search through Typed Lambda-Calculi
Venue: arXiv cs.LO 2021
Year: 2021

In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard paradigm of representation, from proofs to solutions: to represent solutions by possibly infinite terms of a dedicated lambda-calculus. This new, comprehensive approach to proof search is exemplified with the sequent calculus LJT for intuitionistic implication logic. A finitary representation is proposed, comprising lambda-terms extended with a formal greatest fixed point, and a type system that can be seen as a logic of coinductive proofs. In the finitary system, fixed-point variables enjoy a relaxed form of binding that allows the detection of cycles through the type system. Formal sums are used to express alternatives in the search process. Moreover, formal sums are used in the coinductive syntax to define "decontraction" (contraction bottom-up) - an operation whose theory we initiate in this paper. As a semantics, we assign a coinductive lambda-term to each finitary term. The main result is the existence of an equivalent finitary representation for any full solution space expressed coinductively. This result is the main ingredient in the proof that our logic of coinductive proofs is sound and complete with respect to the coinductive semantics. These results are the foundation for an original approach to proof search, where the search builds the finitary representation of the full solution space, and the a posteriori analysis typically consisting in applying a syntax-directed procedure or function. The paper illustrates this for proof search and inhabitation problems in the simply-typed lambda-calculus, reviewing results detailed elsewhere, and including new results that obtain extensive generalizations of the so-called monatomic theorem.
Constraint satisfaction problems for reducts of homogeneous graphs
Venue: arXiv cs.LO 2021
Year: 2021

For $n\geq 3$, let $(H_n, E)$ denote the $n$-th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on $n$ vertices. We show that for all structures $Γ$ with domain $H_n$ whose relations are first-order definable in $(H_n,E)$ the constraint satisfaction problem for $Γ$ is either in P or is NP-complete. We moreover show a similar complexity dichotomy for all structures whose relations are first-order definable in a homogeneous graph whose reflexive closure is an equivalence relation. Together with earlier results, in particular for the random graph, this completes the complexity classification of constraint satisfaction problems of structures first-order definable in countably infinite homogeneous graphs: all such problems are either in P or NP-complete.
Redividing the Cake
Venue: arXiv cs.GT 2021
Year: 2021

The paper considers fair allocation of resources that are already allocated in an unfair way. This setting requires a careful balance between the fairness considerations and the rights of the present owners. The paper presents re-division algorithms that attain various trade-off points between fairness and ownership rights, in various settings differing in the geometric constraints on the allotments: (a) no geometric constraints; (b) connectivity -- the cake is a one-dimensional interval and each piece must be a contiguous interval; (c) rectangularity -- the cake is a two-dimensional rectangle or rectilinear polygon and the pieces should be rectangles; (d) convexity -- the cake is a two-dimensional convex polygon and the pieces should be convex. These re-division algorithms have implications on another problem: the price-of-fairness -- the loss of social welfare caused by fairness requirements. Each algorithm implies an upper bound on the price-of-fairness with the respective geometric constraints.
Efficient Similarity Search in Dynamic Data Streams
Venue: arXiv cs.DS 2021
Year: 2021

The Jaccard index is an important similarity measure for item sets and Boolean data. On large datasets, an exact similarity computation is often infeasible for all item pairs both due to time and space constraints, giving rise to faster approximate methods. The algorithm of choice used to quickly compute the Jaccard index $\frac{\vert A \cap B \vert}{\vert A\cup B\vert}$ of two item sets $A$ and $B$ is usually a form of min-hashing. Most min-hashing schemes are maintainable in data streams processing only additions, but none are known to work when facing item-wise deletions. In this paper, we investigate scalable approximation algorithms for rational set similarities, a broad class of similarity measures including Jaccard. Motivated by a result of Chierichetti and Kumar [J. ACM 2015] who showed any rational set similarity $S$ admits a locality sensitive hashing (LSH) scheme if and only if the corresponding distance $1-S$ is a metric, we can show that there exists a space efficient summary maintaining a $(1\pm \varepsilon)$ multiplicative approximation to $1-S$ in dynamic data streams. This in turn also yields a $\varepsilon$ additive approximation of the similarity. The existence of these approximations hints at, but does not directly imply a LSH scheme in dynamic data streams. Our second and main contribution now lies in the design of such a LSH scheme maintainable in dynamic data streams. The scheme is space efficient, easy to implement and to the best of our knowledge the first of its kind able to process deletions.
On the Effects of Measurement Uncertainty in Optimal Control of Contact Interactions
Venue: arXiv cs.SY 2021
Year: 2021

Stochastic Optimal Control (SOC) typically considers noise only in the process model, i.e. unknown disturbances. However, in many robotic applications involving interaction with the environment, such as locomotion and manipulation, uncertainty also comes from lack of precise knowledge of the world, which is not an actual disturbance. We analyze the effects of also considering noise in the measurement model, by developing a SOC algorithm based on risk-sensitive control, that includes the dynamics of an observer in such a way that the control law explicitly depends on the current measurement uncertainty. In simulation results on a simple 2D manipulator, we have observed that measurement uncertainty leads to low impedance behaviors, a result in contrast with the effects of process noise that creates stiff behaviors. This suggests that taking into account measurement uncertainty could be a potentially very interesting way to approach problems involving uncertain contact interactions.
Enhanced Twitter Sentiment Classification Using Contextual Information
Venue: arXiv cs.SI 2021
Year: 2021

The rise in popularity and ubiquity of Twitter has made sentiment analysis of tweets an important and well-covered area of research. However, the 140 character limit imposed on tweets makes it hard to use standard linguistic methods for sentiment classification. On the other hand, what tweets lack in structure they make up with sheer volume and rich metadata. This metadata includes geolocation, temporal and author information. We hypothesize that sentiment is dependent on all these contextual factors. Different locations, times and authors have different emotional valences. In this paper, we explored this hypothesis by utilizing distant supervision to collect millions of labelled tweets from different locations, times and authors. We used this data to analyse the variation of tweet sentiments across different authors, times and locations. Once we explored and understood the relationship between these variables and sentiment, we used a Bayesian approach to combine these variables with more standard linguistic features such as n-grams to create a Twitter sentiment classifier. This combined classifier outperforms the purely linguistic classifier, showing that integrating the rich contextual information available on Twitter into sentiment classification is a promising direction of research.
Efficient and Compact Representations of Some Non-Canonical Prefix-Free Codes
Venue: arXiv cs.DS 2021
Year: 2021

For many kinds of prefix-free codes there are efficient and compact alternatives to the traditional tree-based representation. Since these put the codes into canonical form, however, they can only be used when we can choose the order in which codewords are assigned to symbols. In this paper we first show how, given a probability distribution over an alphabet of $σ$ symbols, we can store an optimal alphabetic prefix-free code in $\Oh{σ\log L}$ bits such that we can encode and decode any codeword of length $\ell$ in $\Oh{\min (\ell, \log L)}$ time, where $L$ is the maximum codeword length. With $\Oh{2^{L^ε}}$ further bits, for any constant $ε>0$, we can encode and decode $\Oh{\log \ell}$ time. We then show how to store a nearly optimal alphabetic prefix-free code in \(o (σ)\) bits such that we can encode and decode in constant time. We also consider a kind of optimal prefix-free code introduced recently where the codewords' lengths are non-decreasing if arranged in lexicographic order of their reverses. We reduce their storage space to $\Oh{σ\log L}$ while maintaining encoding and decoding times in $\Oh{\ell}$. We also show how, with $\Oh{2^{εL}}$ further bits, we can encode and decode in constant time. All of our results hold in the word-RAM model.
Computing the Optimal Longest Queue Length in Torus Networks
Venue: arXiv cs.DS 2021
Year: 2021

A collection of $k$ mobile agents is arbitrarily deployed in the edges of a directed torus network where agents perpetually move to the successor edge. Each node has a switch that allows one agent of the two incoming edges to pass to its successor edge in every round. The goal is to obtain a switch scheduling to reach and maintain a configuration where the longest queue length is minimum. We consider a synchronous system. We use the concept of conflict graphs to model the local conflicts that occur with incident links. We show that there does not exist an algorithm that can reduce the number of agents in any conflict cycle of the conflict graph providing that all the links have at least 2 agents at every round. Hence, the lower bound is at least the average queue length of the conflict cycle with the maximum average queue length. Next, we present a centralized algorithm that computes a strategy in $O(n\log n)$ time for each round that attains the optimal queue length in $O(σn)$ rounds where $n$ is the number of nodes in the network and $σ$ is the standard deviations of the queue lengths in the initial setting. Our technique is based on network flooding on conflict graphs. Next, we consider a distributed system where nodes have access to the length of their queues and use communication to self-coordinate with nearby nodes. We present a local algorithm using only the information of the queue lengths at distance two. We show that the algorithm attains the optimal queue length in $O(σC_{max}^2)$ rounds where $C_{max}$ is the length of the longest conflict cycle with the maximum average queue length.
Generalised Information Systems Capture L-Domains
Venue: arXiv cs.LO 2021
Year: 2021

A generalisation of Scott's information systems \cite{sco82} is presented that captures exactly all L-domains. The global consistency predicate in Scott's definition is relativised in such a way that there is a consistency predicate for each atomic proposition (token) saying which finite sets of such statements express information that is consistent with the given statement. It is shown that the states of such generalised information systems form an L-domain, and that each L-domain can be generated in this way, up to isomorphism. Moreover, the equivalence of the category of generalised information systems with the category of L-domains is derived. In addition, it will be seen that from every generalised information system capturing an algebraic bounded-complete domain a corresponding Scott information system can be obtained in an easy and natural way, and vice versa; similarly for Hoofman's continuous information systems \cite{ho93} and the continuous bounded-complete domains captured by them; for Chen and Jung's disjunctive propositional logic \cite{cj06} and algebraic L-domains (as well as for Wang and Li's \cite{wll20} finitary version and Lawson-compact algebraic L-domains); and for Wang and Li's conjunctive sequent calculi \cite{wlbc20} and proper continuous bounded-complete domains. The proofs always contain syntactic translations between the logical calculi involved.
Budget Feasible Mechanisms on Matroids
Venue: arXiv cs.GT 2021
Year: 2021

Motivated by many practical applications, in this paper we study {\em budget feasible mechanisms} where the goal is to procure independent sets from matroids. More specifically, we are given a matroid $\mathcal{M}=(E,\mathcal{I})$ where each ground (indivisible) element is a selfish agent. The cost of each element (i.e., for selling the item or performing a service) is only known to the element itself. There is a buyer with a budget having additive valuations over the set of elements $E$. The goal is to design an incentive compatible (truthful) budget feasible mechanism which procures an independent set of the matroid under the given budget that yields the largest value possible to the buyer. Our result is a deterministic, polynomial-time, individually rational, truthful and budget feasible mechanism with $4$-approximation to the optimal independent set. Then, we extend our mechanism to the setting of matroid intersections in which the goal is to procure common independent sets from multiple matroids. We show that, given a polynomial time deterministic blackbox that returns $α-$approximation solutions to the matroid intersection problem, there exists a deterministic, polynomial time, individually rational, truthful and budget feasible mechanism with $(3α+1)-$approximation to the optimal common independent set.
Best Laid Plans of Lions and Men
Venue: arXiv cs.CG 2021
Year: 2021

We study the following question dating back to J.E. Littlewood (1885-1977): Can two lions catch a man in a bounded area with rectifiable lakes? The lions and the man are all assumed to be points moving with at most unit speed. That the lakes are rectifiable means that their boundaries are finitely long. This requirement is necessary to avoid pathological examples where the man survives forever because any path to the lions is infinitely long. We show that three lions have a winning strategy against a man in a bounded region with finitely many rectifiable lakes. This is "tight" in the sense that there exists a region $R$ in the plane where the man has a strategy to survive forever. We give a rigorous description of such a region $R$; a polygonal region with holes whose exterior and interior boundaries are pairwise disjoint, simple polygons. Finally, we consider the following game played on the entire plane instead of a compact region: There is any finite number of unit speed lions and one fast man who can run with speed $1+\varepsilon$ for some value $\varepsilon>0$. Can the man always survive? We answer the question in the affirmative for any $\varepsilon>0$. By letting the number of lions tend to infinity, we furthermore show that the man can survive against any countably infinite set of lions.
$\mathcal{E}\text{psolute}$: Efficiently Querying Databases While Providing Differential Privacy
Venue: arXiv cs.CR 2021
Year: 2021

As organizations struggle with processing vast amounts of information, outsourcing sensitive data to third parties becomes a necessity. To protect the data, various cryptographic techniques are used in outsourced database systems to ensure data privacy, while allowing efficient querying. A rich collection of attacks on such systems has emerged. Even with strong cryptography, just communication volume or access pattern is enough for an adversary to succeed. In this work we present a model for differentially private outsourced database system and a concrete construction, $\mathcal{E}\text{psolute}$, that provably conceals the aforementioned leakages, while remaining efficient and scalable. In our solution, differential privacy is preserved at the record level even against an untrusted server that controls data and queries. $\mathcal{E}\text{psolute}$ combines Oblivious RAM and differentially private sanitizers to create a generic and efficient construction. We go further and present a set of improvements to bring the solution to efficiency and practicality necessary for real-world adoption. We describe the way to parallelize the operations, minimize the amount of noise, and reduce the number of network requests, while preserving the privacy guarantees. We have run an extensive set of experiments, dozens of servers processing up to 10 million records, and compiled a detailed result analysis proving the efficiency and scalability of our solution. While providing strong security and privacy guarantees we are less than an order of magnitude slower than range query execution of a non-secure plain-text optimized RDBMS like MySQL and PostgreSQL.
Complete Call-by-Value Calculi of Control Operators II: Strong Termination
Venue: arXiv cs.LO 2021
Year: 2021

We provide characterization of the strong termination property of the CCV (complete call-by-value) lambda-mu calculus introduced in the first part of this series of the paper. The calculus is complete with respect to the standard continuation-passing style (CPS) semantics. The union-intersection type systems for the calculus is developed in the previous paper. We characterize the strong normalizability of terms of the calculus in terms of the CPS semantics and typeability.
Testing bounded arboricity
Venue: arXiv cs.DS 2021
Year: 2021

In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs with bounded treewidth) and randomly generated preferential attachment graphs. Graphs with bounded arboricity have been studied extensively in the past, in particular since for many problems they allow for much more efficient algorithms and/or better approximation ratios. We present a tolerant tester in the sparse-graphs model. The sparse-graphs model allows access to degree queries and neighbor queries, and the distance is defined with respect to the actual number of edges. More specifically, our algorithm distinguishes between graphs that are $ε$-close to having arboricity $α$ and graphs that $c \cdot ε$-far from having arboricity $3α$, where $c$ is an absolute small constant. The query complexity and running time of the algorithm are $\tilde{O}\left(\frac{n}{\sqrt{m}}\cdot \frac{\log(1/ε)}ε + \frac{n\cdot α}{m} \cdot \left(\frac{1}ε\right)^{O(\log(1/ε))}\right)$ where $n$ denotes the number of vertices and $m$ denotes the number of edges. In terms of the dependence on $n$ and $m$ this bound is optimal up to poly-logarithmic factors since $Ω(n/\sqrt{m})$ queries are necessary (and $α= O(\sqrt{m}))$. We leave it as an open question whether the dependence on $1/ε$ can be improved from quasi-polynomial to polynomial. Our techniques include an efficient local simulation for approximating the outcome of a global (almost) forest-decomposition algorithm as well as a tailored procedure of edge sampling.