Sublinear-Time Algorithms for Monomer-Dimer Systems on Bounded Degree Graphs

For a graph $G$, let $Z(G,\lambda)$ be the partition function of the monomer-dimer system defined by $\sum_k m_k(G)\lambda^k$, where $m_k(G)$ is the number of matchings of size $k$ in $G$. We consider graphs of bounded degree and develop a sublinear-time algorithm for estimating $\log Z(G,\lambda)$ at an arbitrary value $\lambda>0$ within additive error $\epsilon n$ with high probability. The query complexity of our algorithm does not depend on the size of $G$ and is polynomial in $1/\epsilon$, and we also provide a lower bound quadratic in $1/\epsilon$ for this problem. This is the first analysis of a sublinear-time approximation algorithm for a # P-complete problem. Our approach is based on the correlation decay of the Gibbs distribution associated with $Z(G,\lambda)$. We show that our algorithm approximates the probability for a vertex to be covered by a matching, sampled according to this Gibbs distribution, in a near-optimal sublinear time. We extend our results to approximate the average size and the entropy of such a matching within an additive error with high probability, where again the query complexity is polynomial in $1/\epsilon$ and the lower bound is quadratic in $1/\epsilon$. Our algorithms are simple to implement and of practical use when dealing with massive datasets. Our results extend to other systems where the correlation decay is known to hold as for the independent set problem up to the critical activity

Epidemiology of Traveler's Diarrhea

Among travelers from developed countries who visit developing countries, >60% may experience traveler' diarrhea, accounting for 40,000 travelers daily or >15 million travelers annually. Traveler' diarrhea is often accompanied by other symptoms, most often abdominal cramps. Although the spontaneous cure occurs after a mean of 4 days, a few patients have symptoms for weeks, and it is increasingly noted that some patients may later develop irritable bowel syndrome. Traveler' diarrhea is life threatening only exceptionally, but it frequently it leads to incapacitation. Both host factors (e.g., age, behavior, nationality, and genetic factors) and environmental factors (primarily the selected destination and hotel) play an important role in risk for traveler' diarrhe

Information Security in a Quantum World

ISSN:0302-9743ISSN:1611-334

Some Results on Matchgates and Holographic Algorithms

We establish a 1-1 correspondence between Valiant’s character theory of matchgate/matchcircuit [14] and his signature theory of planar-matchgate/matchgrid [16], thus unifying the two theories in expressibility. In [5], we had established a complete characterization of general matchgates, in terms of a set of useful Grassmann-Plücker identities. With this correspondence, we give a corresponding set of identities which completely characterizes planar-matchgates and their signatures. Applying this characterization we prove some negative results for holographic algorithms. On the positive side, we also give a polynomial time algorithm for a simultaneous node-edge deletion problem, using holographic algorithms

Gambling, Computational Information and Encryption Security

We revisit the question, originally posed by Yao (1982), of whether encryption security may be characterized using computational information. Yao provided an affirmative answer, using a compression-based notion of computational information to give a characterization equivalent to the standard computational notion of semantic security. We give two other equivalent charac-terizations. The first uses a computational formulation of Kelly’s (1957) model for “gambling with inside information”, leading to an encryption notion which is similar to Yao’s but where encrypted data is used by an adversary to place bets maximizing the rate of growth of total wealth over a sequence of independent, identically distributed events. The difficulty of this gambling task is closely related to Vadhan and Zheng’s (2011) notion of KL-hardness, which in certain cases is equivalent to a conditional form of the pseudoentropy introduced by Has-tad et. al. (1999). Using techniques introduced to prove this equivalence, we are also able to give a characterization of encryption security in terms of conditional pseudoentropy. Finally, we reconsider the gambling model with respect to “risk-neutral ” adversaries in an attempt to understand whether assumptions about the rationality of adversaries may impact the level of security achieved by an encryption scheme.

A quantum cipher with near optimal key-recycling

Assuming an insecure quantum channel and an authenticated classical channel, we propose an unconditionally secure scheme for encrypting classical messages under a shared key, where attempts to eavesdrop the ciphertext can be detected. If no eavesdropping is detected, we can securely re-use the entire key for encrypting new messages. If eavesdropping is detected, we must discard a number of key bits corresponding to the length of the message, but can re-use almost all of the rest. We show this is essentially optimal. Thus, provided the adversary does not interfere (too much) with the quantum channel, we can securely send an arbitrary number of message bits, independently of the length of the initial key. Moreover, the key-recycling mechanism only requires one-bit feedback. While ordinary quantum key distribution with a classical one time pad could be used instead to obtain a similar functionality, this would need more rounds of interaction and more communication

Closest pair and the post office problem for stochastic points

Abstract. Given a (master) set M of n points in d-dimensional Euclidean space, consider drawing a random subset that includes each point mi ∈ M with an independent probability pi. How difficult is it to compute elementary statistics about the closest pair of points in such a subset? For instance, what is the probability that the distance between the closest pair of points in the random subset is no more than ℓ, for a given value ℓ? Or, can we preprocess the master set M such that given a query point q, we can efficiently estimate the expected distance from q to its nearest neighbor in the random subset? We obtain hardness results and approximation algorithms for stochastic problems of this kind.

Extractors Using Hardness Amplification

Zimand [24] presented simple constructions of locally computable strong extractors whose analysis relies on the direct product theorem for one-way functions and on the Blum-Micali-Yao generator. For N-bit sources of entropy γN, his extractor has seed O(log 2 N)and extracts N γ/3 random bits. We show that his construction can be analyzed based solely on the direct product theorem for general functions. Using the direct product theorem of Impagliazzo et al. [6], we show that Zimand’s construction can extract ˜ Ωγ(N 1/3) random bits. (As in Zimand’s construction, the seed length is O(log 2 N)bits.) We also show that a simplified construction can be analyzed based solely on the XOR lemma. Using Levin’s proof of the XOR lemma [8], we provide an alternative simpler construction of a locally computable extractor with seed length O(log 2 N) and output length ˜ Ωγ(N 1/3). Finally, we show that the derandomized direct product theorem of Impagliazzo and Wigderson [7] can be used to derive a locally computable extractor construction with O(log N) seed length and ˜ Ω(N 1/5) output length. Zimand describes a construction with O(log N) seed length and O(2 √ log N) output length

2007 Global IEEE Telecommunications Conference (GLOBECOM \'07)

The adaptation of structured P2P networks, i.e. Distributed Hash Tables (DHTs), to wireless ad-hoc networks has been investigated in recent years. Existing work assume all peers would come to an agreement on establishing one uniform DHT across the entire network. However, in reality, there isn?t a defacto standard of DHT implementation, different DHTs co-exist. We present a novel protocol, known as the DHT-gatewaying model, which enables cross-DHT searching between multiple DHTs of different implementations