OpenRaiser/Intern-Atlas huggingface dataset:
The Hardness of the Functional Orientation 2-Color Problem
Venue: arXiv cs.CC 2013
Year: 2013

We consider the Functional Orientation 2-Color problem, which was introduced by Valiant in his seminal paper on holographic algorithms [SIAM J. Comput., 37(5), 2008]. For this decision problem, Valiant gave a polynomial time holographic algorithm for planar graphs of maximum degree 3, and showed that the problem is NP-complete for planar graphs of maximum degree 10. A recent result on defective graph coloring by Corrêa et al. [Australas. J. Combin., 43, 2009] implies that the problem is already hard for planar graphs of maximum degree 8. Together, these results leave open the hardness question for graphs of maximum degree between 4 and 7. We close this gap by showing that the answer is always yes for arbitrary graphs of maximum degree 5, and that the problem is NP-complete for planar graphs of maximum degree 6. Moreover, for graphs of maximum degree 5, we note that a linear time algorithm for finding a solution exists.
Hyperplane Separation Technique for Multidimensional Mean-Payoff Games
Venue: arXiv cs.GT 2013
Year: 2013

We consider both finite-state game graphs and recursive game graphs (or pushdown game graphs), that can model the control flow of sequential programs with recursion, with multi-dimensional mean-payoff objectives. In pushdown games two types of strategies are relevant: global strategies, that depend on the entire global history; and modular strategies, that have only local memory and thus do not depend on the context of invocation. We present solutions to several fundamental algorithmic questions and our main contributions are as follows: (1) We show that finite-state multi-dimensional mean-payoff games can be solved in polynomial time if the number of dimensions and the maximal absolute value of the weight is fixed; whereas if the number of dimensions is arbitrary, then problem is already known to be coNP-complete. (2) We show that pushdown graphs with multi-dimensional mean-payoff objectives can be solved in polynomial time. (3) For pushdown games under global strategies both single and multi-dimensional mean-payoff objectives problems are known to be undecidable, and we show that under modular strategies the multi-dimensional problem is also undecidable (whereas under modular strategies the single dimensional problem is NP-complete). We show that if the number of modules, the number of exits, and the maximal absolute value of the weight is fixed, then pushdown games under modular strategies with single dimensional mean-payoff objectives can be solved in polynomial time, and if either of the number of exits or the number of modules is not bounded, then the problem is NP-hard. (4) Finally we show that a fixed parameter tractable algorithm for finite-state multi-dimensional mean-payoff games or pushdown games under modular strategies with single-dimensional mean-payoff objectives would imply the solution of the long-standing open problem of fixed parameter tractability of parity games.
Coalgebraic Analysis of Subgame-perfect Equilibria in Infinite Games without Discounting
Venue: arXiv cs.GT 2013
Year: 2013

We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame perfect equilibria using a novel proof principle of predicate coinduction. We characterize all subgame perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the payoffs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics.
A Truthful Auction based Incentive Framework for Femtocell Access
Venue: arXiv cs.GT 2013
Year: 2013

As cellular operators are suffering from a data explosion problem, and users are consequently experiencing poor data services, the introduction of femtocells offers a cost-effective way to mitigate this problem. Femtocells enable larger network capacity by increasing spatial reuse of the spectrum and shortening the distance to the users. Existing work has shown that open access femtocells, which allow unregistered macro users to connect, are efficient in reducing inter-cell interference and offloading traffic. However, a major obstacle constraining the potential capability of femtocells and open access is the lack of incentives for privately-owned femtocells to serve unregistered users. Hence in this paper, we propose a Vickrey-Clarke-Groves (VCG) auction based incentive framework for accessing such selfish femtocells. We consider two scenarios: One scenario involves a single macro user and another scenario has multiple macro users. We design auction schemes for both scenarios and show analytically that our schemes are truthful and have low computational complexity. Extensive simulations validate these properties and show huge performance improvement to the macro users.
A Generalization of Lee Codes
Venue: arXiv cs.DM 2013
Year: 2013

Motivated by a problem in computer architecture we introduce a notion of the perfect distance-dominating set, PDDS, in a graph. PDDSs constitute a generalization of perfect Lee codes, diameter perfect codes, as well as other codes and dominating sets. In this paper we initiate a systematic study of PDDSs. PDDSs related to the application will be constructed and the non-existence of some PDDSs will be shown. In addition, an extension of the long-standing Golomb-Welch conjecture, in terms of PDDS, will be stated. We note that all constructed PDDSs are lattice-like which is a very important feature from the practical point of view as in this case decoding algorithms tend to be much simpler.
Accelerating Iterative Detection for Spatially Coupled Systems by Collaborative Training
Venue: arXiv cs.IT 2013
Year: 2013

This letter proposes a novel method for accelerating iterative detection for spatially coupled (SC) systems. An SC system is constructed by one-dimensional coupling of many subsystems, which are classified into training and propagation parts. An irregular structure is introduced into the subsystems in the training part so that information in that part can be detected successfully. The obtained reliable information may spread over the whole system via the subsystems in the propagation part. In order to allow the subsystems in the training part to collaborate, shortcuts between them are created to accelerate iterative detection for that part. As an example of SC systems, SC code-division multiple-access (CDMA) systems are considered. Density Evolution for the SC CDMA systems shows that the proposed method can provide a significant reduction in the number of iterations for highly loaded systems.
Link Scheduling in Amplify-and-Forward Cooperative Wireless Networks
Venue: arXiv cs.NI 2013
Year: 2013

In this work we are concerned with the problem of link scheduling for throughput maximization in wireless networks that employ a cooperative amplify and forward (AF) protocol. To address this problem first we define the signal-to-interference plus noise ratio (SINR) expression for the complete cooperative AF-based transmission. Next, we formulate the problem of link scheduling as a mixed integer linear program (MILP) that uses as a constraint the developed SINR expression. The proposed formulation is motivated by the observation that the aggregate interference that affects a single cooperative transmission can be decomposed into two separate SINR constraints. Results for the optimal solution and a polynomial time approximation algorithm are also presented.
Time-Space Trade-Offs for Longest Common Extensions
Venue: arXiv cs.DS 2013
Year: 2013

We revisit the longest common extension (LCE) problem, that is, preprocess a string $T$ into a compact data structure that supports fast LCE queries. An LCE query takes a pair $(i,j)$ of indices in $T$ and returns the length of the longest common prefix of the suffixes of $T$ starting at positions $i$ and $j$. We study the time-space trade-offs for the problem, that is, the space used for the data structure vs. the worst-case time for answering an LCE query. Let $n$ be the length of $T$. Given a parameter $τ$, $1 \leq τ\leq n$, we show how to achieve either $O(\infrac{n}{\sqrtτ})$ space and $O(τ)$ query time, or $O(\infrac{n}τ)$ space and $O(τ\log({|\LCE(i,j)|}/τ))$ query time, where $|\LCE(i,j)|$ denotes the length of the LCE returned by the query. These bounds provide the first smooth trade-offs for the LCE problem and almost match the previously known bounds at the extremes when $τ=1$ or $τ=n$. We apply the result to obtain improved bounds for several applications where the LCE problem is the computational bottleneck, including approximate string matching and computing palindromes. We also present an efficient technique to reduce LCE queries on two strings to one string. Finally, we give a lower bound on the time-space product for LCE data structures in the non-uniform cell probe model showing that our second trade-off is nearly optimal.
A Note on Circular Arc Online Coloring using First Fit
Venue: arXiv cs.DS 2013
Year: 2013

In Raman (2007), using a column construction technique it is proved that every interval graph can be colored online with First Fit with at most $8w(G)$ colors, where $w(G)$ is the size of the maximum clique of $G$. Since the column construction can not be adapted to circular arc graphs we give a different proof to establish an upper bound of $9w(G)$ for online coloring a circular arc graph $G$ with the First Fit algorithm.
Differential Privacy for the Analyst via Private Equilibrium Computation
Venue: arXiv cs.DS 2013
Year: 2013

We give new mechanisms for answering exponentially many queries from multiple analysts on a private database, while protecting differential privacy both for the individuals in the database and for the analysts. That is, our mechanism's answer to each query is nearly insensitive to changes in the queries asked by other analysts. Our mechanism is the first to offer differential privacy on the joint distribution over analysts' answers, providing privacy for data analysts even if the other data analysts collude or register multiple accounts. In some settings, we are able to achieve nearly optimal error rates (even compared to mechanisms which do not offer analyst privacy), and we are able to extend our techniques to handle non-linear queries. Our analysis is based on a novel view of the private query-release problem as a two-player zero-sum game, which may be of independent interest.
Algorithm Runtime Prediction: Methods & Evaluation
Venue: arXiv cs.AI 2013
Year: 2013

Perhaps surprisingly, it is possible to predict how long an algorithm will take to run on a previously unseen input, using machine learning techniques to build a model of the algorithm's runtime as a function of problem-specific instance features. Such models have important applications to algorithm analysis, portfolio-based algorithm selection, and the automatic configuration of parameterized algorithms. Over the past decade, a wide variety of techniques have been studied for building such models. Here, we describe extensions and improvements of existing models, new families of models, and -- perhaps most importantly -- a much more thorough treatment of algorithm parameters as model inputs. We also comprehensively describe new and existing features for predicting algorithm runtime for propositional satisfiability (SAT), travelling salesperson (TSP) and mixed integer programming (MIP) problems. We evaluate these innovations through the largest empirical analysis of its kind, comparing to a wide range of runtime modelling techniques from the literature. Our experiments consider 11 algorithms and 35 instance distributions; they also span a very wide range of SAT, MIP, and TSP instances, with the least structured having been generated uniformly at random and the most structured having emerged from real industrial applications. Overall, we demonstrate that our new models yield substantially better runtime predictions than previous approaches in terms of their generalization to new problem instances, to new algorithms from a parameterized space, and to both simultaneously.
Low-Latency Data Sharing in Erasure Multi-Way Relay Channels
Venue: arXiv cs.IT 2013
Year: 2013

We consider an erasure multi-way relay channel (EMWRC) in which several users share their data through a relay over erasure links. Assuming no feedback channel between the users and the relay, we first identify the challenges for designing a data sharing scheme over an EMWRC. Then, to overcome these challenges, we propose practical low-latency and low-complexity data sharing schemes based on fountain coding. Later, we introduce the notion of end-to-end erasure rate (EEER) and analytically derive it for the proposed schemes. EEER is then used to calculate the achievable rate and transmission overhead of the proposed schemes. Using EEER and computer simulations, the achievable rates and transmission overhead of our proposed schemes are compared with the ones of one-way relaying. This comparison implies that when the number of users and the channel erasure rates are not large, our proposed schemes outperform one-way relaying. We also find an upper bound on the achievable rates of EMWRC and observe that depending on the number of users and channel erasure rates, our proposed solutions can perform very close to this bound.
Hybrid Behaviour of Markov Population Models
Venue: arXiv cs.SY 2013
Year: 2013

We investigate the behaviour of population models written in Stochastic Concurrent Constraint Programming (sCCP), a stochastic extension of Concurrent Constraint Programming. In particular, we focus on models from which we can define a semantics of sCCP both in terms of Continuous Time Markov Chains (CTMC) and in terms of Stochastic Hybrid Systems, in which some populations are approximated continuously, while others are kept discrete. We will prove the correctness of the hybrid semantics from the point of view of the limiting behaviour of a sequence of models for increasing population size. More specifically, we prove that, under suitable regularity conditions, the sequence of CTMC constructed from sCCP programs for increasing population size converges to the hybrid system constructed by means of the hybrid semantics. We investigate in particular what happens for sCCP models in which some transitions are guarded by boolean predicates or in the presence of instantaneous transitions.
S2LET: A code to perform fast wavelet analysis on the sphere
Venue: arXiv cs.IT 2013
Year: 2013

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended features of signals on the sphere. The scale-discretised wavelet transform was developed previously and reduces to the needlet transform in the axisymmetric case. The reconstruction of a signal from its wavelets coefficients is made exact here through the use of a sampling theorem on the sphere. Moreover, a multiresolution algorithm is presented to capture all information of each wavelet scale in the minimal number of samples on the sphere. In addition S2LET supports the HEALPix pixelisation scheme, in which case the transform is not exact but nevertheless achieves good numerical accuracy. The core routines of S2LET are written in C and have interfaces in Matlab, IDL and Java. Real signals can be written to and read from FITS files and plotted as Mollweide projections. The S2LET code is made publicly available, is extensively documented, and ships with several examples in the four languages supported. At present the code is restricted to axisymmetric wavelets but will be extended to directional, steerable wavelets in a future release.
Codes with Local Regeneration
Venue: arXiv cs.IT 2013
Year: 2013

Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node, regenerating codes seek to minimize the amount of data downloaded for node repair, while codes with locality attempt to minimize the number of helper nodes accessed. In this paper, we provide several constructions for a class of vector codes with locality in which the local codes are regenerating codes, that enjoy both advantages. We derive an upper bound on the minimum distance of this class of codes and show that the proposed constructions achieve this bound. The constructions include both the cases where the local regenerating codes correspond to the MSR as well as the MBR point on the storage-repair-bandwidth tradeoff curve of regenerating codes. Also included is a performance comparison of various code constructions for fixed block length and minimum distance.
An Efficient Encryption Algorithm for P2P Networks Robust Against Man-in-the-Middle Adversary
Venue: arXiv cs.CR 2013
Year: 2013

Peer-to-peer (P2P) networks have become popular as a new paradigm for information exchange and are being used in many applications such as file sharing, distributed computing, video conference, VoIP, radio and TV broadcasting. This popularity comes with security implications and vulnerabilities that need to be addressed. Especially duo to direct communication between two end nodes in P2P networks, these networks are potentially vulnerable to "Man-in-the-Middle" attacks. In this paper, we propose a new public-key cryptosystem for P2P networks that is robust against Man-in-the-Middle adversary. This cryptosystem is based on RSA and knapsack problems. Our precoding-based algorithm uses knapsack problem for performing permutation and padding random data to the message. We show that comparing to other proposed cryptosystems, our algorithm is more efficient and it is fully secure against an active adversary.
Context-Driven Elicitation of Default Requirements: an Empirical Validation
Venue: arXiv cs.SE 2013
Year: 2013

In Requirements Engineering, requirements elicitation aims the acquisition of information from the stakeholders of a system-to-be. An important task during elicitation is to identify and render explicit the stakeholders' implicit assumptions about the system-to-be and its environment. Purpose of doing so is to identify omissions in, and conflicts between requirements. This paper offers a conceptual framework for the identification and documentation of default requirements that stakeholders may be using. The framework is relevant for practice, as it forms a check-list for types of questions to use during elicitation. An empirical validation is described, and guidelines for elicitation are drawn.
Near-Optimal Distributed Scheduling Algorithms for Regular Wireless Sensor Networks
Venue: arXiv cs.NI 2013
Year: 2013

Wireless sensor networks are normally characterized by resource challenged nodes. Since communication costs the most in terms of energy in these networks, minimizing this overhead is important. We consider minimum length node scheduling in regular multi-hop wireless sensor networks. We present collision-free decentralized scheduling algorithms based on TDMA with spatial reuse that do not use message passing, this saving communication overhead. We develop the algorithms using graph-based k-hop interference model and show that the schedule complexity in regular networks is independent of the number of nodes and varies quadratically with k which is typically a very small number. We follow it by characterizing feasibility regions in the SINR parameter space where the constant complexity continues to hold while simultaneously satisfying the SINR criteria. Using simulation, we evaluate the efficiency of our solution on random network deployments.
Gap Processing for Adaptive Maximal Poisson-Disk Sampling
Venue: arXiv cs.GR 2013
Year: 2013

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.
Accelerated Canonical Polyadic Decomposition by Using Mode Reduction
Venue: arXiv cs.NA 2013
Year: 2013

Canonical Polyadic (or CANDECOMP/PARAFAC, CP) decompositions (CPD) are widely applied to analyze high order tensors. Existing CPD methods use alternating least square (ALS) iterations and hence need to unfold tensors to each of the $N$ modes frequently, which is one major bottleneck of efficiency for large-scale data and especially when $N$ is large. To overcome this problem, in this paper we proposed a new CPD method which converts the original $N$th ($N>3$) order tensor to a 3rd-order tensor first. Then the full CPD is realized by decomposing this mode reduced tensor followed by a Khatri-Rao product projection procedure. This way is quite efficient as unfolding to each of the $N$ modes are avoided, and dimensionality reduction can also be easily incorporated to further improve the efficiency. We show that, under mild conditions, any $N$th-order CPD can be converted into a 3rd-order case but without destroying the essential uniqueness, and theoretically gives the same results as direct $N$-way CPD methods. Simulations show that, compared with state-of-the-art CPD methods, the proposed method is more efficient and escape from local solutions more easily.
Unified Form Language: A domain-specific language for weak formulations of partial differential equations
Venue: arXiv cs.MS 2013
Year: 2013

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies for multi-field problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted.