OpenRaiser/Intern-Atlas huggingface dataset:
Episodic Multi-armed Bandits
Venue: arXiv cs.LG 2018
Year: 2018

We introduce a new class of reinforcement learning methods referred to as {\em episodic multi-armed bandits} (eMAB). In eMAB the learner proceeds in {\em episodes}, each composed of several {\em steps}, in which it chooses an action and observes a feedback signal. Moreover, in each step, it can take a special action, called the $stop$ action, that ends the current episode. After the $stop$ action is taken, the learner collects a terminal reward, and observes the costs and terminal rewards associated with each step of the episode. The goal of the learner is to maximize its cumulative gain (i.e., the terminal reward minus costs) over all episodes by learning to choose the best sequence of actions based on the feedback. First, we define an {\em oracle} benchmark, which sequentially selects the actions that maximize the expected immediate gain. Then, we propose our online learning algorithm, named {\em FeedBack Adaptive Learning} (FeedBAL), and prove that its regret with respect to the benchmark is bounded with high probability and increases logarithmically in expectation. Moreover, the regret only has polynomial dependence on the number of steps, actions and states. eMAB can be used to model applications that involve humans in the loop, ranging from personalized medical screening to personalized web-based education, where sequences of actions are taken in each episode, and optimal behavior requires adapting the chosen actions based on the feedback.
Technical Note: Split Algorithm in O(n) for the Capacitated Vehicle Routing Problem
Venue: arXiv cs.DS 2018
Year: 2018

The Split algorithm is an essential building block of route-first cluster-second heuristics and modern genetic algorithms for vehicle routing problems. The algorithm is used to partition a solution, represented as a giant tour without occurrences of the depot, into separate routes with minimum cost. As highlighted by the recent survey of [Prins, Lacomme and Prodhon, Transport Res. C (40), 179-200], no less than 70 recent articles use this technique. In the vehicle routing literature, Split is usually assimilated to the search for a shortest path in a directed acyclic graph $\mathcal{G}$ and solved in $O(nB)$ using Bellman's algorithm, where $n$ is the number of delivery points and $B$ is the average number of feasible routes that start with a given customer in the giant tour. Some linear-time algorithms are also known for this problem as a consequence of a Monge property of $\mathcal{G}$. In this article, we highlight a stronger property of this graph, leading to a simple alternative algorithm in $O(n)$. Experimentally, we observe that the approach is faster than the classical Split for problem instances of practical size. We also extend the method to deal with a limited fleet and soft capacity constraints.
Randomised enumeration of small witnesses using a decision oracle
Venue: arXiv cs.DS 2018
Year: 2018

Many combinatorial problems involve determining whether a universe of $n$ elements contains a witness consisting of $k$ elements which have some specified property. In this paper we investigate the relationship between the decision and enumeration versions of such problems: efficient methods are known for transforming a decision algorithm into a search procedure that finds a single witness, but even finding a second witness is not so straightforward in general. We show that, if the decision version of the problem can be solved in time $f(k) \cdot poly(n)$, there is a randomised algorithm which enumerates all witnesses in time $e^{k + o(k)} \cdot f(k) \cdot poly(n) \cdot N$, where $N$ is the total number of witnesses. If the decision version of the problem is solved by a randomised algorithm which may return false negatives, then the same method allows us to output a list of witnesses in which any given witness will be included with high probability. The enumeration algorithm also gives rise to an efficient algorithm to count the total number of witnesses when this number is small.
Using Contracted Solution Graphs for Solving Reconfiguration Problems
Venue: arXiv cs.DS 2018
Year: 2018

We introduce in a general setting a dynamic programming method for solving reconfiguration problems. Our method is based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions that decrease the graph size without losing any critical information needed to solve the reconfiguration problem under consideration. Our general framework captures the approach behind known reconfiguration results of Bonsma (2012) and Hatanaka, Ito and Zhou (2014). As a third example, we apply the method to the following problem: given two $k$-colorings $α$ and $β$ of a graph $G$, can $α$ be modified into $β$ by recoloring one vertex of $G$ at a time, while maintaining a $k$-coloring throughout? This problem is known to be PSPACE-hard even for bipartite planar graphs and $k=4$. By applying our method in combination with a thorough exploitation of the graph structure we obtain a polynomial time algorithm for $(k-2)$-connected chordal graphs.
A faster subquadratic algorithm for finding outlier correlations
Venue: arXiv cs.DS 2018
Year: 2018

We study the problem of detecting outlier pairs of strongly correlated variables among a collection of $n$ variables with otherwise weak pairwise correlations. After normalization, this task amounts to the geometric task where we are given as input a set of $n$ vectors with unit Euclidean norm and dimension $d$, and for some constants $0<τ<ρ<1$, we are asked to find all the outlier pairs of vectors whose inner product is at least $ρ$ in absolute value, subject to the promise that all but at most $q$ pairs of vectors have inner product at most $τ$ in absolute value. Improving on an algorithm of G. Valiant [FOCS 2012; J. ACM 2015], we present a randomized algorithm that for Boolean inputs ($\{-1,1\}$-valued data normalized to unit Euclidean length) runs in time \[ \tilde O\bigl(n^{\max\,\{1-γ+M(Δγ,γ),\,M(1-γ,2Δγ)\}}+qdn^{2γ}\bigr)\,, \] where $0<γ<1$ is a constant tradeoff parameter and $M(μ,ν)$ is the exponent to multiply an $\lfloor n^μ\rfloor\times\lfloor n^ν\rfloor$ matrix with an $\lfloor n^ν\rfloor\times \lfloor n^μ\rfloor$ matrix and $Δ=1/(1-\log_τρ)$. As corollaries we obtain randomized algorithms that run in time \[ \tilde O\bigl(n^{\frac{2ω}{3-\log_τρ}}+qdn^{\frac{2(1-\log_τρ)}{3-\log_τρ}}\bigr) \] and in time \[ \tilde O\bigl(n^{\frac{4}{2+α(1-\log_τρ)}}+qdn^{\frac{2α(1-\log_τρ)}{2+α(1-\log_τρ)}}\bigr)\,, \] where $2\leqω<2.38$ is the exponent for square matrix multiplication and $0.3<α\leq 1$ is the exponent for rectangular matrix multiplication. The notation $\tilde O(\cdot)$ hides polylogarithmic factors in $n$ and $d$ whose degree may depend on $ρ$ and $τ$. We present further corollaries for the light bulb problem and for learning sparse Boolean functions.
Surface Approximation via Asymptotic Optimal Geometric Partition
Venue: arXiv cs.GR 2018
Year: 2018

In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra curvature metric field for the desired anisotropy to best approximate the surface, even though the estimated curvature metric is known to be imperfect and already self-contained in the surface. In our approach, this anisotropic control is achieved through the optimal geometry partition without this explicit metric field. The minimization of our proposed partition energy has the following properties: Firstly, on a C2 surface, it is theoretically guaranteed to have the optimal aspect ratio and cluster size as specified in approximation theory for L1 piecewise linear approximation. Secondly, it captures sharp features on practical models without any pre-tagging. We develop an effective merging-swapping framework to seek the optimal partition and construct polygonal/triangular mesh afterwards. The effectiveness and efficiency of our method are demonstrated through the comparison with other state-of-the-art remeshing methods.
Abelian logic gates
Venue: arXiv cs.DM 2018
Year: 2018

An abelian processor is an automaton whose output is independent of the order of its inputs. Bond and Levine have proved that a network of abelian processors performs the same computation regardless of processing order (subject only to a halting condition). We prove that any finite abelian processor can be emulated by a network of certain very simple abelian processors, which we call gates. The most fundamental gate is a "toppler", which absorbs input particles until their number exceeds some given threshold, at which point it topples, emitting one particle and returning to its initial state. With the exception of an adder gate, which simply combines two streams of particles, each of our gates has only one input wire. Our results can be reformulated in terms of the functions computed by processors, and one consequence is that any increasing function from N^k to N^l that is the sum of a linear function and a periodic function can be expressed in terms of (possibly nested) sums of floors of quotients by integers.
Stable Matching Mechanisms are Not Obviously Strategy-Proof
Venue: arXiv cs.GT 2018
Year: 2018

Many two-sided matching markets, from labor markets to school choice programs, use a clearinghouse based on the applicant-proposing deferred acceptance algorithm, which is well known to be strategy-proof for the applicants. Nonetheless, a growing amount of empirical evidence reveals that applicants misrepresent their preferences when this mechanism is used. This paper shows that no mechanism that implements a stable matching is "obviously strategy-proof" for any side of the market, a stronger incentive property than strategy-proofness that was introduced by Li (2017). A stable mechanism that is obviously strategy-proof for applicants is introduced for the case in which agents on the other side have acyclical preferences.
Uniqueness, Spatial Mixing, and Approximation for Ferromagnetic 2-Spin Systems
Venue: arXiv cs.DS 2018
Year: 2018

We give fully polynomial-time approximation schemes (FPTAS) for the partition function of ferromagnetic 2-spin systems in certain parameter regimes. The threshold we obtain is almost tight up to an integrality gap. Our technique is based on the correlation decay framework. The main technical contribution is a new potential function, with which we establish a new kind of spatial mixing.
Constant-approximation algorithms for highly connected multi-dominating sets in unit disk graphs
Venue: arXiv cs.DS 2018
Year: 2018

Given an undirected graph on a node set $V$ and positive integers $k$ and $m$, a $k$-connected $m$-dominating set ($(k,m)$-CDS) is defined as a subset $S$ of $V$ such that each node in $V \setminus S$ has at least $m$ neighbors in $S$, and a $k$-connected subgraph is induced by $S$. The weighted $(k,m)$-CDS problem is to find a minimum weight $(k,m)$-CDS in a given node-weighted graph. The problem is called the unweighted $(k,m)$-CDS problem if the objective is to minimize the cardinality of a $(k,m)$-CDS. These problems have been actively studied for unit disk graphs, motivated by the application of constructing a virtual backbone in a wireless ad hoc network. However, constant-approximation algorithms are known only for $k \leq 3$ in the unweighted $(k,m)$-CDS problem, and for $(k,m)=(1,1)$ in the weighted $(k,m)$-CDS problem. In this paper, we consider the case in which $m \geq k$, and we present a simple $O(5^k k!)$-approximation algorithm for the unweighted $(k,m)$-CDS problem, and a primal-dual $O(k^2 \log k)$-approximation algorithm for the weighted $(k,m)$-CDS problem. Both algorithms achieve constant approximation factors when $k$ is a fixed constant.
Technical Privacy Metrics: a Systematic Survey
Venue: arXiv cs.CR 2018
Year: 2018

The goal of privacy metrics is to measure the degree of privacy enjoyed by users in a system and the amount of protection offered by privacy-enhancing technologies. In this way, privacy metrics contribute to improving user privacy in the digital world. The diversity and complexity of privacy metrics in the literature makes an informed choice of metrics challenging. As a result, instead of using existing metrics, new metrics are proposed frequently, and privacy studies are often incomparable. In this survey we alleviate these problems by structuring the landscape of privacy metrics. To this end, we explain and discuss a selection of over eighty privacy metrics and introduce categorizations based on the aspect of privacy they measure, their required inputs, and the type of data that needs protection. In addition, we present a method on how to choose privacy metrics based on nine questions that help identify the right privacy metrics for a given scenario, and highlight topics where additional work on privacy metrics is needed. Our survey spans multiple privacy domains and can be understood as a general framework for privacy measurement.
Vector Network Coding Based on Subspace Codes Outperforms Scalar Linear Network Coding
Venue: arXiv cs.IT 2018
Year: 2018

This paper considers vector network coding solutions based on rank-metric codes and subspace codes. The main result of this paper is that vector solutions can significantly reduce the required alphabet size compared to the optimal scalar linear solution for the same multicast network. The multicast networks considered in this paper have one source with $h$ messages, and the vector solution is over a field of size $q$ with vectors of length~$t$. For a given network, let the smallest field size for which the network has a scalar linear solution be $q_s$, then the gap in the alphabet size between the vector solution and the scalar linear solution is defined to be $q_s-q^t$. In this contribution, the achieved gap is $q^{(h-2)t^2/h + o(t)}$ for any $q \geq 2$ and any even $h \geq 4$. If $h \geq 5$ is odd, then the achieved gap of the alphabet size is $q^{(h-3)t^2/(h-1) + o(t)}$. Previously, only a gap of size size one had been shown for networks with a very large number of messages. These results imply the same gap of the alphabet size between the optimal scalar linear and some scalar nonlinear network coding solution for multicast networks. For three messages, we also show an advantage of vector network coding, while for two messages the problem remains open. Several networks are considered, all of them are generalizations and modifications of the well-known combination networks. The vector network codes that are used as solutions for those networks are based on subspace codes, particularly subspace codes obtained from rank-metric codes. Some of these codes form a new family of subspace codes, which poses a new research problem.
On tensor products of CSS Codes
Venue: arXiv cs.IT 2018
Year: 2018

CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product $\otimes$ which induces a similar operation on the former. We investigate this operation, and in particular its behavior with regard to minimum distances. Given a CSS code $\mathcal{C}$, we give a criterion which provides a lower bound on the minimum distance of $\mathcal{C} \otimes \mathcal{D}$ for every CSS code $\mathcal D$. We apply this result to study the behaviour of iterated tensor powers of codes. Such sequences of codes are logarithmically LDPC and we prove in particular that their minimum distances tend generically to infinity. Different known results are reinterpretated in terms of tensor products. Three new families of CSS codes are defined, and their iterated tensor powers produce LDPC sequences of codes with length $n$, row weight in $O(\log n)$ and minimum distances larger than $n^{\fracα{2}}$ for any $α<1$. One family produces sequences with dimensions larger than $n^β$ for any $β<1$.
A Learning Algorithm for Change Impact Prediction
Venue: arXiv cs.SE 2018
Year: 2018

Change impact analysis consists in predicting the impact of a code change in a software application. In this paper, we take a learning perspective on change impact analysis and consider the problem formulated as follows. The artifacts that are considered are methods of object-oriented software, the change under study is a change in the code of the method, the impact is the test methods that fail because of the change that has been performed. We propose an algorithm, called LCIP that learns from past impacts to predict future impacts. To evaluate our system, we consider 7 Java software applications totaling 214,000+ lines of code. We simulate 17574 changes and their actual impact through code mutations, as done in mutation testing. We find that LCIP can predict the impact with a precision of 69%, a recall of 79%, corresponding to a F-Score of 55%.
Decremental Single-Source Shortest Paths on Undirected Graphs in Near-Linear Total Update Time
Venue: arXiv cs.DS 2018
Year: 2018

In the decremental single-source shortest paths (SSSP) problem we want to maintain the distances between a given source node $s$ and every other node in an $n$-node $m$-edge graph $G$ undergoing edge deletions. While its static counterpart can be solved in near-linear time, this decremental problem is much more challenging even in the undirected unweighted case. In this case, the classic $O(mn)$ total update time of Even and Shiloach [JACM 1981] has been the fastest known algorithm for three decades. At the cost of a $(1+ε)$-approximation factor, the running time was recently improved to $n^{2+o(1)}$ by Bernstein and Roditty [SODA 2011]. In this paper, we bring the running time down to near-linear: We give a $(1+ε)$-approximation algorithm with $m^{1+o(1)}$ expected total update time, thus obtaining near-linear time. Moreover, we obtain $m^{1+o(1)} \log W$ time for the weighted case, where the edge weights are integers from $1$ to $W$. The only prior work on weighted graphs in $o(m n)$ time is the $m n^{0.9 + o(1)}$-time algorithm by Henzinger et al. [STOC 2014, ICALP 2015] which works for directed graphs with quasi-polynomial edge weights. The expected running time bound of our algorithm holds against an oblivious adversary. In contrast to the previous results which rely on maintaining a sparse emulator, our algorithm relies on maintaining a so-called sparse $(h, ε)$-hop set introduced by Cohen [JACM 2000] in the PRAM literature. An $(h, ε)$-hop set of a graph $G=(V, E)$ is a set $F$ of weighted edges such that the distance between any pair of nodes in $G$ can be $(1+ε)$-approximated by their $h$-hop distance (given by a path containing at most $h$ edges) on $G'=(V, E\cup F)$. Our algorithm can maintain an $(n^{o(1)}, ε)$-hop set of near-linear size in near-linear time under edge deletions.
Approximating the Distribution of the Median and other Robust Estimators on Uncertain Data
Venue: arXiv cs.DM 2018
Year: 2018

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has a discrete probability distribution describing its location. The probabilistic nature of uncertain data makes it challenging to compute such estimators, since the true value of the estimator is now described by a distribution rather than a single point. We show how to construct and estimate the distribution of the median of a point set. Building the approximate support of the distribution takes near-linear time, and assigning probability to that support takes quadratic time. We also develop a general approximation technique for distributions of robust estimators with respect to ranges with bounded VC dimension. This includes the geometric median for high dimensions and the Siegel estimator for linear regression.
Distortion Bounds for Source Broadcast Problems
Venue: arXiv cs.IT 2018
Year: 2018

This paper investigates the joint source-channel coding problem of sending a memoryless source over a memoryless broadcast channel. An inner bound and several outer bounds on the admissible distortion region are derived, which respectively generalize and unify several existing bounds. As a consequence, we also obtain an inner bound and an outer bound for the degraded broadcast channel case. When specialized to the Gaussian or binary source broadcast, the inner bound and outer bound not only recover the best known inner bound and outer bound in the literature, but also generate some new results. Besides, we also extend the inner bound and outer bounds to the Wyner-Ziv source broadcast problem, i.e., source broadcast with side information available at decoders. Some new bounds are obtained when specialized to the Wyner-Ziv Gaussian and Wyner-Ziv binary cases.
Identity Testing for Constant-Width, and Any-Order, Read-Once Oblivious Arithmetic Branching Programs
Venue: arXiv cs.CC 2018
Year: 2018

We give improved hitting sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known order of the variables. The best previously known hitting set for this case had size $(nw)^{O(\log n)}$ where $n$ is the number of variables and $w$ is the width of the ROABP. Even for a constant-width ROABP, nothing better than a quasi-polynomial bound was known. We improve the hitting-set size for the known-order case to $n^{O(\log w)}$. In particular, this gives the first polynomial-size hitting set for constant-width ROABP (known-order). However, our hitting set only works when the characteristic of the field is zero or large enough. To construct the hitting set, we use the concept of the rank of the partial derivative matrix. Unlike previous approaches which build up from mapping variables to monomials, we map variables to polynomials directly. The second case we consider is that of polynomials computable by width-$w$ ROABPs in any order of the variables. The best previously known hitting set for this case had size $d^{O(\log w)}(nw)^{O(\log \log w)}$, where $d$ is the individual degree. We improve the hitting-set size to $(ndw)^{O(\log \log w)}$.
Walsh Sampling with Incomplete Noisy Signals
Venue: arXiv cs.IT 2018
Year: 2018

With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources as well. Under the general assumption of discrete statistical signal sources, we propose a practical problem of sampling incomplete noisy signals for which we do not know a priori and the sampling size is bounded. We approach this sampling problem by Shannon's channel coding theorem. Our main results demonstrate that it is the large Walsh coefficient(s) that characterize(s) discrete statistical signals, regardless of the signal sources. By the connection of Shannon's theorem, we establish the necessary and sufficient condition for our generic sampling problem for the first time. Our generic sampling results find practical and powerful applications in not only statistical cryptanalysis, but software system performance optimization.