OpenRaiser/Intern-Atlas huggingface dataset:
REESSE1+ . Reward . Proof by Experiment . A New Approach to Proof of P != NP
Venue: arXiv cs.CR 2014
Year: 2014

The authors discuss what is provable security in cryptography. Think that provable security is asymptotic, relative, and dynamic, and only a supplement to but not a replacement of exact security analysis. Because the conjecture P != NP has not been proven yet, and it is possible in terms of the two incompleteness theorems of Kurt Godel that there is some cryptosystem of which the security cannot or only ideally be proven in the random oracle model, the security of a cryptosystem is between provability and unprovability, and any academic conclusion must be checked and verified with practices or experiments as much as possible. Extra, a new approach to proof of P != NP is pointed out. Lastly, a reward is offered for the subexponential time solutions to the three REESSE1+ problems: MPP, ASPP, and TLP with n >= 80 and lg M >= 80, which may be regarded as a type of security proof by experiment.
Quantization Errors of Modulo Sigma-Delta Modulated ARMA Processes
Venue: arXiv cs.IT 2014
Year: 2014

In this paper, we study the quantization errors of modulo sigma-delta modulated finite, asymptotically-infinite, infinite causal stable ARMA processes. We prove that the normalized quantization error can be taken as a uniformly distributed white noise for all the cases. Moreover, we find that this nice property is guaranteed by two different mechanisms: the high-enough quantization resolution \cite{Bennett1948}-\cite{WidrowKollar2008} and the asymptotic convergence of quantization errors for some quasi-stationary processes \cite{ChouGray1991}-\cite{LiChenLiZhang2009}, for different cases. But the assumption of the smooth density of the sampled random processes is needed in all the cases.
Faster and simpler approximation of stable matchings
Venue: arXiv cs.DS 2014
Year: 2014

We give a 3/2-approximation algorithm for stable matchings that runs in $O(m)$ time. The previously best known algorithm by McDermid has the same approximation ratio but runs in $O(n^{3/2}m)$ time, where $n$ denotes the number of people and $m$ is the total length of the preference lists in a given instance. Also the algorithm and the analysis are much simpler. We also give the extension of the algorithm for the many-to-many setting. (This is the version of the paper from March 2011)
Duality, Polite Water-filling, and Optimization for MIMO B-MAC Interference Networks and iTree Networks
Venue: arXiv cs.IT 2014
Year: 2014

This paper gives the long sought network version of water-filling named as polite water-filling. Unlike in single-user MIMO channels, where no one uses general purpose optimization algorithms in place of the simple and optimal water-filling for transmitter optimization, the traditional water-filling is generally far from optimal in networks as simple as MIMO multiaccess channels (MAC) and broadcast channels (BC), where steepest ascent algorithms have been used except for the sum-rate optimization. This is changed by the polite water-filling that is optimal for all boundary points of the capacity regions of MAC and BC and for all boundary points of a set of achievable regions of a more general class of MIMO B-MAC interference networks, which is a combination of multiple interfering broadcast channels, from the transmitter point of view, and multiaccess channels, from the receiver point of view, including MAC, BC, interference channels, X networks, and most practical wireless networks as special case. It is polite because it strikes an optimal balance between reducing interference to others and maximizing a link's own rate. Employing it, the related optimizations can be vastly simplified by taking advantage of the structure of the problems. Deeply connected to the polite water-filling, the rate duality is extended to the forward and reverse links of the B-MAC networks. As a demonstration, weighted sum-rate maximization algorithms based on polite water-filling and duality with superior performance and low complexity are designed for B-MAC networks and are analyzed for Interference Tree (iTree) Networks, a sub-class of the B-MAC networks that possesses promising properties for further information theoretic study.
The space complexity of recognizing well-parenthesized expressions in the streaming model: the Index function revisited
Venue: arXiv cs.CC 2014
Year: 2014

We show an Omega(sqrt{n}/T) lower bound for the space required by any unidirectional constant-error randomized T-pass streaming algorithm that recognizes whether an expression over two types of parenthesis is well-parenthesized. This proves a conjecture due to Magniez, Mathieu, and Nayak (2009) and rigorously establishes that bidirectional streams are exponentially more efficient in space usage as compared with unidirectional ones. We obtain the lower bound by establishing the minimum amount of information that is necessarily revealed by the players about their respective inputs in a two-party communication protocol for a variant of the Index function, namely Augmented Index. The information cost trade-off is obtained by a novel application of the conceptually simple and familiar ideas such as average encoding and the cut-and-paste property of randomized protocols. Motivated by recent examples of exponential savings in space by streaming quantum algorithms, we also study quantum protocols for Augmented Index. Defining an appropriate notion of information cost for quantum protocols involves a delicate balancing act between its applicability and the ease with which we can analyze it. We define a notion of quantum information cost which reflects some of the non-intuitive properties of quantum information and give a trade-off for this notion. While this trade-off demonstrates the strength of our proof techniques, it does not lead to a space lower bound for checking parentheses. We leave such an implication for quantum streaming algorithms as an intriguing open question.
Improved Direct Product Theorems for Randomized Query Complexity
Venue: arXiv cs.CC 2014
Year: 2014

The direct product problem is a fundamental question in complexity theory which seeks to understand how the difficulty of computing a function on each of k independent inputs scales with k. We prove the following direct product theorem (DPT) for query complexity: if every T-query algorithm has success probability at most 1 - eps in computing the Boolean function f on input distribution Mu, then for alpha <= 1, every (alpha eps Tk)-query algorithm has success probability at most (2^{alpha eps}(1 - eps))^k in computing the k-fold direct product f^k correctly on k independent inputs from Mu. In light of examples due to Shaltiel, this statement gives an essentially optimal tradeoff between the query bound and the error probability. As a corollary, we show that for an absolute constant alpha > 0, the worst-case success probability of any (alpha R_2(f)k)-query randomized algorithm for f^k falls exponentially with k. The best previous statement of this type, due to Klauck, Spalek, and de Wolf, required a query bound of O(bs(f)k). The proof involves defining and analyzing a collection of martingales associated with an algorithm attempting to solve f^k. Our method is quite general and yields a new XOR lemma and threshold DPT for the query model, as well as DPTs for the query complexity of learning tasks, search problems, and tasks involving interaction with dyamic entities. We also give a version of our DPT in which decision tree size is the resource of interest.
On the Relation between Realizable and Nonrealizable Cases of the Sequence Prediction Problem
Venue: arXiv cs.LG 2014
Year: 2014

A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $μ$. After observing each outcome, one is required to give conditional probabilities of the next observation. The realizable case is when the measure $μ$ belongs to an arbitrary but known class $\mathcal C$ of process measures. The non-realizable case is when $μ$ is completely arbitrary, but the prediction performance is measured with respect to a given set $\mathcal C$ of process measures. We are interested in the relations between these problems and between their solutions, as well as in characterizing the cases when a solution exists and finding these solutions. We show that if the quality of prediction is measured using the total variation distance, then these problems coincide, while if it is measured using the expected average KL divergence, then they are different. For some of the formalizations we also show that when a solution exists, it can be obtained as a Bayes mixture over a countable subset of $\mathcal C$. We also obtain several characterization of those sets $\mathcal C$ for which solutions to the considered problems exist. As an illustration to the general results obtained, we show that a solution to the non-realizable case of the sequence prediction problem exists for the set of all finite-memory processes, but does not exist for the set of all stationary processes. It should be emphasized that the framework is completely general: the processes measures considered are not required to be i.i.d., mixing, stationary, or to belong to any parametric family.
Delay and Redundancy in Lossless Source Coding
Venue: arXiv cs.IT 2014
Year: 2014

The penalty incurred by imposing a finite delay constraint in lossless source coding of a memoryless source is investigated. It is well known that for the so-called block-to-variable and variable-to-variable codes, the redundancy decays at best polynomially with the delay, where in this case the delay is identified with the source block length or maximal source phrase length, respectively. In stark contrast, it is shown that for sequential codes (e.g., a delay-limited arithmetic code) the redundancy can be made to decay exponentially with the delay constraint. The corresponding redundancy-delay exponent is shown to be at least as good as the Rényi entropy of order 2 of the source, but (for almost all sources) not better than a quantity depending on the minimal source symbol probability and the alphabet size.
Adaptive Event Dissemination for Peer-to-Peer Multiplayer Online Games
Venue: arXiv cs.NI 2014
Year: 2014

In this paper we show that gossip algorithms may be effectively used to disseminate game events in Peer-to-Peer (P2P) Multiplayer Online Games (MOGs). Game events are disseminated through an overlay network. The proposed scheme exploits the typical behavior of players to tune the data dissemination. In fact, it is well known that users playing a MOG typically generate game events at a rate that can be approximated using some (game dependent) probability distribution. Hence, as soon as a given node experiences a reception rate, for messages coming from a given peer, which is lower than expected, it can send a stimulus to the neighbor that usually forwards these messages, asking it to increase its dissemination probability. Three variants of this approach will be studied. According to the first one, upon reception of a stimulus from a neighbor, a peer increases its dissemination probability towards that node irrespectively from the sender. In the second protocol a peer increases only the dissemination probability for a given sender towards all its neighbors. Finally, the third protocol takes into consideration both the sender and the neighbor in order to decide how to increase the dissemination probability. We performed extensive simulations to assess the efficacy of the proposed scheme, and based on the simulation results we compare the different dissemination protocols. The results confirm that adaptive gossip schemes are indeed effective and deserve further investigation.
A Self-Organized Resource Allocation using Inter-Cell Interference Coordination (ICIC) in Relay-Assisted Cellular Networks
Venue: arXiv cs.NI 2014
Year: 2014

In a multi-cell scenario, the inter-cell interference (ICI) is detrimental in achieving the intended system performance, in particular for the edge users. There is paucity of work available in literature on ICI coordination (ICIC) for relay-assisted cellular networks (RACN). In this paper, we do a survey on the ICIC schemes in cellular networks and RACN. We then propose a self-organized resource allocation plan for RACN to improve the edge user's performance by ICIC. We compare the performance of reuse-1, reuse-3, soft frequency reuse (SFR) scheme, proposed plan with and without relays. The performance metrics for comparison are edge user's spectral efficiency, their signal-to-interference-and-noise ratio (SINR) and system's area spectral efficiency. We show by the simulation results that our proposed plan performs better than the existing resource allocation schemes in static allocation scenario. Next, we propose to make our resource allocation plan dynamic and self-organized. The distinct features of our proposed plan are: One, it achieves a trade-off between the system's area spectral efficiency and the edge user's spectral efficiency performance. Secondly, it introduces a novel concept of interfering neighbor set to achieve ICIC by local interaction between the entities.
LUNES: Agent-based Simulation of P2P Systems (Extended Version)
Venue: arXiv cs.DC 2014
Year: 2014

We present LUNES, an agent-based Large Unstructured NEtwork Simulator, which allows to simulate complex networks composed of a high number of nodes. LUNES is modular, since it splits the three phases of network topology creation, protocol simulation and performance evaluation. This permits to easily integrate external software tools into the main software architecture. The simulation of the interaction protocols among network nodes is performed via a simulation middleware that supports both the sequential and the parallel/distributed simulation approaches. In the latter case, a specific mechanism for the communication overhead-reduction is used; this guarantees high levels of performance and scalability. To demonstrate the efficiency of LUNES, we test the simulator with gossip protocols executed on top of networks (representing peer-to-peer overlays), generated with different topologies. Results demonstrate the effectiveness of the proposed approach.
The Chaos of Propagation in a Retrial Supermarket Model
Venue: arXiv cs.NI 2014
Year: 2014

When decomposing the total orbit into $N$ sub-orbits (or simply orbits) related to each of $N$ servers and through comparing the numbers of customers in these orbits, we introduce a retrial supermarket model of $N$ identical servers, where two probing-server choice numbers are respectively designed for dynamically allocating each primary arrival and each retrial arrival into these orbits when the chosen servers are all busy. Note that the designed purpose of the two choice numbers can effectively improve performance measures of this retrial supermarket model. This paper analyzes a simple and basic retrial supermarket model of N identical servers, that is, Poisson arrivals, exponential service and retrial times. To this end, we first provide a detailed probability computation to set up an infinite-dimensional system of differential equations (or mean-field equations) satisfied by the expected fraction vector. Then, as N goes to infinity, we apply the operator semigroup to obtaining the mean-field limit (or chaos of propagation) for the sequence of Markov processes which express the state of this retrial supermarket model. Specifically, some simple and basic conditions for the mean-field limit as well as for the Lipschitz condition are established through the first two moments of the queue length in any orbit. Finally, we show that the fixed point satisfies a system of nonlinear equations which is an interesting networking generalization of the tail equations given in the M/M/1 retrial queue, and also use the fixed point to give performance analysis of this retrial supermarket model through numerical computation.
Learning $k$-Modal Distributions via Testing
Venue: arXiv cs.DS 2014
Year: 2014

A $k$-modal probability distribution over the discrete domain $\{1,...,n\}$ is one whose histogram has at most $k$ "peaks" and "valleys." Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability distributions, which have been intensively studied in probability theory and statistics. In this paper we consider the problem of \emph{learning} (i.e., performing density estimation of) an unknown $k$-modal distribution with respect to the $L_1$ distance. The learning algorithm is given access to independent samples drawn from an unknown $k$-modal distribution $p$, and it must output a hypothesis distribution $\widehat{p}$ such that with high probability the total variation distance between $p$ and $\widehat{p}$ is at most $ε.$ Our main goal is to obtain \emph{computationally efficient} algorithms for this problem that use (close to) an information-theoretically optimal number of samples. We give an efficient algorithm for this problem that runs in time $\mathrm{poly}(k,\log(n),1/ε)$. For $k \leq \tilde{O}(\log n)$, the number of samples used by our algorithm is very close (within an $\tilde{O}(\log(1/ε))$ factor) to being information-theoretically optimal. Prior to this work computationally efficient algorithms were known only for the cases $k=0,1$ \cite{Birge:87b,Birge:97}. A novel feature of our approach is that our learning algorithm crucially uses a new algorithm for \emph{property testing of probability distributions} as a key subroutine. The learning algorithm uses the property tester to efficiently decompose the $k$-modal distribution into $k$ (near-)monotone distributions, which are easier to learn.
From Small-World Networks to Comparison-Based Search
Venue: arXiv cs.LG 2014
Year: 2014

The problem of content search through comparisons has recently received considerable attention. In short, a user searching for a target object navigates through a database in the following manner: the user is asked to select the object most similar to her target from a small list of objects. A new object list is then presented to the user based on her earlier selection. This process is repeated until the target is included in the list presented, at which point the search terminates. This problem is known to be strongly related to the small-world network design problem. However, contrary to prior work, which focuses on cases where objects in the database are equally popular, we consider here the case where the demand for objects may be heterogeneous. We show that, under heterogeneous demand, the small-world network design problem is NP-hard. Given the above negative result, we propose a novel mechanism for small-world design and provide an upper bound on its performance under heterogeneous demand. The above mechanism has a natural equivalent in the context of content search through comparisons, and we establish both an upper bound and a lower bound for the performance of this mechanism. These bounds are intuitively appealing, as they depend on the entropy of the demand as well as its doubling constant, a quantity capturing the topology of the set of target objects. They also illustrate interesting connections between comparison-based search to classic results from information theory. Finally, we propose an adaptive learning algorithm for content search that meets the performance guarantees achieved by the above mechanisms.
Quantization of Binary-Input Discrete Memoryless Channels
Venue: arXiv cs.IT 2014
Year: 2014

The quantization of the output of a binary-input discrete memoryless channel to a smaller number of levels is considered. An algorithm which finds an optimal quantizer, in the sense of maximizing mutual information between the channel input and the quantizer output is given. This result holds for arbitrary channels, in contrast to previous results for restricted channels or a restricted number of quantizer outputs. In the worst case, the algorithm complexity is cubic $M^3$ in the number of channel outputs $M$. Optimality is proved using the theorem of Burshtein, Della Pietra, Kanevsky, and Nádas for mappings which minimize average impurity for classification and regression trees.
Distributed Agreement in Dynamic Peer-to-Peer Networks
Venue: arXiv cs.DS 2014
Year: 2014

Motivated by the need for robust and fast distributed computation in highly dynamic Peer-to-Peer (P2P) networks, we study algorithms for the fundamental distributed agreement problem. P2P networks are highly dynamic networks that experience heavy node {\em churn}. Our goal is to design fast algorithms (running in a small number of rounds) that guarantee, despite high node churn rate, that almost all nodes reach a stable agreement. Our main contributions are randomized distributed algorithms that guarantee {\em stable almost-everywhere agreement} with high probability even under high adversarial churn in a polylogarithmic number of rounds: 1. An $O(\log^2 n)$-round ($n$ is the stable network size) randomized algorithm that achieves almost-everywhere agreement with high probability under up to {\em linear} churn {\em per round} (i.e., $εn$, for some small constant $ε> 0$), assuming that the churn is controlled by an oblivious adversary (that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm). Our algorithm requires only polylogarithmic in $n$ bits to be processed and sent (per round) by each node. 2. An $O(\log m\log^3 n)$-round randomized algorithm that achieves almost-everywhere agreement with high probability under up to $ε\sqrt{n}$ churn per round (for some small $ε> 0$), where $m$ is the size of the input value domain, that works even under an adaptive adversary (that also knows the past random choices made by the algorithm). This algorithm requires up to polynomial in $n$ bits (and up to $O(\log m)$ bits) to be processed and sent (per round) by each node.
Auction-Based Resource Allocation in Digital Ecosystems
Venue: arXiv cs.DC 2014
Year: 2014

The proliferation of portable devices (PDAs, smartphones, digital multimedia players, and so forth) allows mobile users to carry around a pool of computing, storage and communication resources. Sharing these resources with other users ("Digital Organisms" -- DOs) opens the door to novel interesting scenarios, where people trade resources to allow the execution, anytime and anywhere, of applications that require a mix of capabilities. In this paper we present a fully distributed approach for resource sharing among multiple devices owned by different mobile users. Our scheme enables DOs to trade computing/networking facilities through an auction-based mechanism, without the need of a central control. We use a set of numerical experiments to compare our approach with an optimal (centralized) allocation strategy that, given the set of resource demands and offers, maximizes the number of matches. Results confirm the effectiveness of our approach since it produces a fair allocation of resources with low computational cost, providing DOs with the means to form an altruistic digital ecosystem.