OpenRaiser/Intern-Atlas huggingface dataset:
Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of a C Program
Venue: arXiv cs.LO 2012
Year: 2012

We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.
Reidentification and k-anonymity: a model for disclosure risk in graphs
Venue: arXiv cs.CR 2012
Year: 2012

In this article we provide a formal framework for reidentification in general. We define n-confusion as a concept for modelling the anonymity of a database table and we prove that n-confusion is a generalization of k- anonymity. After a short survey on the different available definitions of k- anonymity for graphs we provide a new definition for k-anonymous graph, which we consider to be the correct definition. We provide a description of the k-anonymous graphs, both for the regular and the non-regular case. We also introduce the more flexible concept of (k,l)-anonymous graph. Our definition of (k,l)-anonymous graph is meant to replace a previous definition of (k, l)-anonymous graph, which we here prove to have severe weaknesses. Finally we provide a set of algorithms for k-anonymization of graphs.
Chinese Restaurant Game - Part I: Theory of Learning with Negative Network Externality
Venue: arXiv cs.SI 2012
Year: 2012

In a social network, agents are intelligent and have the capability to make decisions to maximize their utilities. They can either make wise decisions by taking advantages of other agents' experiences through learning, or make decisions earlier to avoid competitions from huge crowds. Both these two effects, social learning and negative network externality, play important roles in the decision process of an agent. While there are existing works on either social learning or negative network externality, a general study on considering both these two contradictory effects is still limited. We find that the Chinese restaurant process, a popular random process, provides a well-defined structure to model the decision process of an agent under these two effects. By introducing the strategic behavior into the non-strategic Chinese restaurant process, in Part I of this two-part paper, we propose a new game, called Chinese Restaurant Game, to formulate the social learning problem with negative network externality. Through analyzing the proposed Chinese restaurant game, we derive the optimal strategy of each agent and provide a recursive method to achieve the optimal strategy. How social learning and negative network externality influence each other under various settings is also studied through simulations.
Steiner Forest Orientation Problems
Venue: arXiv cs.DS 2012
Year: 2012

We consider connectivity problems with orientation constraints. Given a directed graph $D$ and a collection of ordered node pairs $P$ let $P[D]=\{(u,v) \in P: D {contains a} uv{-path}}$. In the {\sf Steiner Forest Orientation} problem we are given an undirected graph $G=(V,E)$ with edge-costs and a set $P \subseteq V \times V$ of ordered node pairs. The goal is to find a minimum-cost subgraph $H$ of $G$ and an orientation $D$ of $H$ such that $P[D]=P$. We give a 4-approximation algorithm for this problem. In the {\sf Maximum Pairs Orientation} problem we are given a graph $G$ and a multi-collection of ordered node pairs $P$ on $V$. The goal is to find an orientation $D$ of $G$ such that $|P[D]|$ is maximum. Generalizing the result of Arkin and Hassin [DAM'02] for $|P|=2$, we will show that for a mixed graph $G$ (that may have both directed and undirected edges), one can decide in $n^{O(|P|)}$ time whether $G$ has an orientation $D$ with $P[D]=P$ (for undirected graphs this problem admits a polynomial time algorithm for any $P$, but it is NP-complete on mixed graphs). For undirected graphs, we will show that one can decide whether $G$ admits an orientation $D$ with $|P[D]| \geq k$ in $O(n+m)+2^{O(k\cdot \log \log k)}$ time; hence this decision problem is fixed-parameter tractable, which answers an open question from Dorn et al. [AMB'11]. We also show that {\sf Maximum Pairs Orientation} admits ratio $O(\log |P|/\log\log |P|)$, which is better than the ratio $O(\log n/\log\log n)$ of Gamzu et al. [WABI'10] when $|P|<n$. Finally, we show that the following node-connectivity problem can be solved in polynomial time: given a graph $G=(V,E)$ with edge-costs, $s,t \in V$, and an integer $\ell$, find a min-cost subgraph $H$ of $G$ with an orientation $D$ such that $D$ contains $\ell$ internally-disjoint $st$-paths, and $\ell$ internally-disjoint $ts$-paths.
Competition and Regulation in Wireless Services Markets
Venue: arXiv cs.NI 2012
Year: 2012

We consider a wireless services market where a set of operators compete for a large common pool of users. The latter have a reservation utility of U0 units or, equivalently, an alternative option to satisfy their communication needs. The operators must satisfy these minimum requirements in order to attract the users. We model the users decisions and interaction as an evolutionary game and the competition among the operators as a non cooperative price game which is proved to be a potential game. For each set of prices selected by the operators, the evolutionary game attains a different stationary point. We show that the outcome of both games depend on the reservation utility of the users and the amount of spectrum W the operators have at their disposal. We express the market welfare and the revenue of the operators as functions of these two parameters. Accordingly, we consider the scenario where a regulating agency is able to intervene and change the outcome of the market by tuning W and/or U0. Different regulators may have different objectives and criteria according to which they intervene. We analyze the various possible regulation methods and discuss their requirements, implications and impact on the market.
Improving Noise Robustness in Subspace-based Joint Sparse Recovery
Venue: arXiv cs.IT 2012
Year: 2012

In a multiple measurement vector problem (MMV), where multiple signals share a common sparse support and are sampled by a common sensing matrix, we can expect joint sparsity to enable a further reduction in the number of required measurements. While a diversity gain from joint sparsity had been demonstrated earlier in the case of a convex relaxation method using an $l_1/l_2$ mixed norm penalty, only recently was it shown that similar diversity gain can be achieved by greedy algorithms if we combine greedy steps with a MUSIC-like subspace criterion. However, the main limitation of these hybrid algorithms is that they often require a large number of snapshots or a high signal-to-noise ratio (SNR) for an accurate subspace as well as partial support estimation. One of the main contributions of this work is to show that the noise robustness of these algorithms can be significantly improved by allowing sequential subspace estimation and support filtering, even when the number of snapshots is insufficient. Numerical simulations show that a novel sequential compressive MUSIC (sequential CS-MUSIC) that combines the sequential subspace estimation and support filtering steps significantly outperforms the existing greedy algorithms and is quite comparable with computationally expensive state-of-art algorithms.
Root finding with threshold circuits
Venue: arXiv cs.DS 2012
Year: 2012

We show that for any constant d, complex roots of degree d univariate rational (or Gaussian rational) polynomials---given by a list of coefficients in binary---can be computed to a given accuracy by a uniform TC^0 algorithm (a uniform family of constant-depth polynomial-size threshold circuits). The basic idea is to compute the inverse function of the polynomial by a power series. We also discuss an application to the theory VTC^0 of bounded arithmetic.
Markov Decision Process Based Energy-Efficient On-Line Scheduling for Slice-Parallel Video Decoders on Multicore Systems
Venue: arXiv cs.MM 2012
Year: 2012

We consider the problem of energy-efficient on-line scheduling for slice-parallel video decoders on multicore systems. We assume that each of the processors are Dynamic Voltage Frequency Scaling (DVFS) enabled such that they can independently trade off performance for power, while taking the video decoding workload into account. In the past, scheduling and DVFS policies in multi-core systems have been formulated heuristically due to the inherent complexity of the on-line multicore scheduling problem. The key contribution of this report is that we rigorously formulate the problem as a Markov decision process (MDP), which simultaneously takes into account the on-line scheduling and per-core DVFS capabilities; the power consumption of the processor cores and caches; and the loss tolerant and dynamic nature of the video decoder's traffic. In particular, we model the video traffic using a Direct Acyclic Graph (DAG) to capture the precedence constraints among frames in a Group of Pictures (GOP) structure, while also accounting for the fact that frames have different display/decoding deadlines and non-deterministic decoding complexities. The objective of the MDP is to minimize long-term power consumption subject to a minimum Quality of Service (QoS) constraint related to the decoder's throughput. Although MDPs notoriously suffer from the curse of dimensionality, we show that, with appropriate simplifications and approximations, the complexity of the MDP can be mitigated. We implement a slice-parallel version of H.264 on a multiprocessor ARM (MPARM) virtual platform simulator, which provides cycle-accurate and bus signal-accurate simulation for different processors. We use this platform to generate realistic video decoding traces with which we evaluate the proposed on-line scheduling algorithm in Matlab.
POWERPLAY: Training an Increasingly General Problem Solver by Continually Searching for the Simplest Still Unsolvable Problem
Venue: arXiv cs.AI 2012
Year: 2012

Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. The novel algorithmic framework POWERPLAY (2011) continually searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Wow-effects are achieved by continually making previously learned skills more efficient such that they require less time and space. New skills may (partially) re-use previously learned skills. POWERPLAY's search orders candidate pairs of tasks and solver modifications by their conditional computational (time & space) complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. The computational costs of validating new tasks need not grow with task repertoire size. POWERPLAY's ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Goedel's sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing repertoire of problem solving procedures can be exploited by a parallel search for solutions to additional externally posed tasks. POWERPLAY may be viewed as a greedy but practical implementation of basic principles of creativity. A first experimental analysis can be found in separate papers [53,54].
Memory-Constrained Algorithms for Simple Polygons
Venue: arXiv cs.CG 2012
Year: 2012

A constant-workspace algorithm has read-only access to an input array and may use only O(1) additional words of $O(\log n)$ bits, where $n$ is the size of the input. We assume that a simple $n$-gon is given by the ordered sequence of its vertices. We show that we can find a triangulation of a plane straight-line graph in $O(n^2)$ time. We also consider preprocessing a simple polygon for shortest path queries when the space constraint is relaxed to allow $s$ words of working space. After a preprocessing of $O(n^2)$ time, we are able to solve shortest path queries between any two points inside the polygon in $O(n^2/s)$ time.
Cayley Configuration Spaces of 1-dof Tree-decomposable Linkages, Part II: Combinatorial Characterization of Complexity
Venue: arXiv cs.CG 2012
Year: 2012

We continue to study Cayley configuration spaces of 1-dof linkages in 2D begun in Part I of this paper, i.e. the set of attainable lengths for a non-edge. In Part II, we focus on the algebraic complexity of describing endpoints of the intervals in the set, i.e., the Cayley complexity. Specifically, We focus on Cayley configuration spaces of a natural class of 1-dof linkages, called 1-dof tree-decomposable linkages. The underlying graphs G satisfy the following: for some base non-edge f, G \cup f is quadratic-radically solvable (QRS), meaning that G \cup f is minimally rigid, and given lengths \bar{l} of all edges, the corresponding linkage (G \cup f, \bar{l}) can be simply realized by ruler and compass starting from f. It is clear that the Cayley complexity only depends on the graph G and possibly the non-edge f. Here we ask whether the Cayley complexity depends on the choice of a base non-edge f. We answer this question in the negative, thereby showing that low Cayley complexity is a property of the graph G (independent of the non-edge f). Then, we give a simple characterization of graphs with low Cayley complexity, leading to an efficient algorithmic characterization, i.e. an efficient algorithm for recognizing such graphs. Next, we show a surprising result that (graph) planarity is equivalent to low Cayley complexity for a natural subclass of 1-dof triangle-decomposable graphs. While this is a finite forbidden minor graph characterization of low Cayley complexity, we provide counterexamples showing impossibility of such finite forbidden minor characterizations when the above subclass is enlarged.
Optimal decentralized control of coupled subsystems with control sharing
Venue: arXiv cs.SY 2012
Year: 2012

Subsystems that are coupled due to dynamics and costs arise naturally in various communication applications. In many such applications the control actions are shared between different control stations giving rise to a \emph{control sharing} information structure. Previous studies of control-sharing have concentrated on the linear quadratic Gaussian setup and a solution approach tailored to continuous valued control actions. In this paper a three step solution approach for finite valued control actions is presented. In the first step, a person-by-person approach is used to identify redundant data or a sufficient statistic for local information at each control station. In the second step, the common-information based approach of Nayyar et al.\ (2011) is used to find a sufficient statistic for the common information shared between all control stations and to obtain a dynamic programming decomposition. In the third step, the specifics of the model are used to simplify the sufficient statistic and the dynamic program. As an example, an exact solution of a two-user multiple access broadcast system is presented.
(1+epsilon)-Distance Oracle for Planar Labeled Graph
Venue: arXiv cs.DS 2012
Year: 2012

Given a vertex-labeled graph, each vertex $v$ is attached with a label from a set of labels. The vertex-label query desires the length of the shortest path from the given vertex to the set of vertices with the given label. We show how to construct an oracle if the given graph is planar, such that $O(\frac{1}εn\log n)$ storing space is needed, and any vertex-label query could be answered in $O(\frac{1}ε\log n\log ρ)$ time with stretch $1+ε$. $ρ$ is the radius of the given graph, which is half of the diameter. For the case that $ρ= O(\log n)$, we construct an oracle that achieves $O(\log n)$ query time, without changing the order of storing space.
On the Complexity of Solving Quadratic Boolean Systems
Venue: arXiv cs.SC 2012
Year: 2012

A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over $\mathbb{F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity bound was reached by an exhaustive search in $4\log_2 n\,2^n$ operations. We give an algorithm that reduces the problem to a combination of exhaustive search and sparse linear algebra. This algorithm has several variants depending on the method used for the linear algebra step. Under precise algebraic assumptions on the input system, we show that the deterministic variant of our algorithm has complexity bounded by $O(2^{0.841n})$ when $m=n$, while a probabilistic variant of the Las Vegas type has expected complexity $O(2^{0.792n})$. Experiments on random systems show that the algebraic assumptions are satisfied with probability very close to~1. We also give a rough estimate for the actual threshold between our method and exhaustive search, which is as low as~200, and thus very relevant for cryptographic applications.
The Maximum Clique Problem in Multiple Interval Graphs
Venue: arXiv cs.DM 2012
Year: 2012

Multiple interval graphs are variants of interval graphs where instead of a single interval, each vertex is assigned a set of intervals on the real line. We study the complexity of the MAXIMUM CLIQUE problem in several classes of multiple interval graphs. The MAXIMUM CLIQUE problem, or the problem of finding the size of the maximum clique, is known to be NP-complete for $t$-interval graphs when $t\geq 3$ and polynomial-time solvable when $t=1$. The problem is also known to be NP-complete in $t$-track graphs when $t\geq 4$ and polynomial-time solvable when $t\leq 2$. We show that MAXIMUM CLIQUE is already NP-complete for unit 2-interval graphs and unit 3-track graphs. Further, we show that the problem is APX-complete for 2-interval graphs, 3-track graphs, unit 3-interval graphs and unit 4-track graphs. We also introduce two new classes of graphs called $t$-circular interval graphs and $t$-circular track graphs and study the complexity of the MAXIMUM CLIQUE problem in them. On the positive side, we present a polynomial time $t$-approximation algorithm for WEIGHTED MAXIMUM CLIQUE on $t$-interval graphs, improving earlier work with approximation ratio $4t$.
Hiding Malicious Content in PDF Documents
Venue: arXiv cs.CR 2012
Year: 2012

This paper is a proof-of-concept demonstration for a specific digital signatures vulnerability that shows the ineffectiveness of the WYSIWYS (What You See Is What You Sign) concept. The algorithm is fairly simple: the attacker generates a polymorphic file that has two different types of content (text, as a PDF document for example, and image: TIFF - two of the most widely used file formats). When the victim signs the dual content file, he/ she only sees a PDF document and is unaware of the hidden content inside the file. After obtaining the legally signed document from the victim, the attacker simply has to change the extension to the other file format. This will not invalidate the digital signature, as no bits were altered. The destructive potential of the attack is considerable, as the Portable Document Format (PDF) is widely used in e-government and in e-business contexts.
Pattern Clustering using Cooperative Game Theory
Venue: arXiv cs.GT 2012
Year: 2012

In this paper, we approach the classical problem of clustering using solution concepts from cooperative game theory such as Nucleolus and Shapley value. We formulate the problem of clustering as a characteristic form game and develop a novel algorithm DRAC (Density-Restricted Agglomerative Clustering) for clustering. With extensive experimentation on standard data sets, we compare the performance of DRAC with that of well known algorithms. We show an interesting result that four prominent solution concepts, Nucleolus, Shapley value, Gately point and τ-value coincide for the defined characteristic form game. This vindicates the choice of the characteristic function of the clustering game and also provides strong intuitive foundation for our approach.
Formalizing Traceability and Derivability in Software Product Lines
Venue: arXiv cs.SE 2012
Year: 2012

In the literature, the definition of product in a Software Product Line (SPL) is based upon the notion of consistency of the constraints, imposed by variability and traceability relations on the elements of the SPL. In this paper, we contend that consistency does not model the natural semantics of the implementability relation between problem and solution spaces correctly. Therefore, we define when a feature can be {\em derived} from a set of components . Using this, we define a product of the SPL by a <specification, architecture> pair, where all the features in the specification are derived from the components in the architecture. This notion of derivability is formulated in a simple yet expressive, abstract model of a productline with traceability relation. We then define a set of SPL analysis problems and show that these problems can be encoded as Quantified Boolean Formulas. Then, QSAT solvers like QUBE can be used to solve the analysis problems. We illustrate the methodology on a small fragment of a realistic productline.
Interactive multiview video system with non-complex navigation at the decoder
Venue: arXiv cs.MM 2012
Year: 2012

Multiview video with interactive and smooth view switching at the receiver is a challenging application with several issues in terms of effective use of storage and bandwidth resources, reactivity of the system, quality of the viewing experience and system complexity. The classical decoding system for generating virtual views first projects a reference or encoded frame to a given viewpoint and then fills in the holes due to potential occlusions. This last step still constitutes a complex operation with specific software or hardware at the receiver and requires a certain quantity of information from the neighboring frames for insuring consistency between the virtual images. In this work we propose a new approach that shifts most of the burden due to interactivity from the decoder to the encoder, by anticipating the navigation of the decoder and sending auxiliary information that guarantees temporal and interview consistency. This leads to an additional cost in terms of transmission rate and storage, which we minimize by using optimization techniques based on the user behavior modeling. We show by experiments that the proposed system represents a valid solution for interactive multiview systems with classical decoders.