On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint

In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and $v$ in $G$, the number of internal nodes on the shortest path between $u$ and $v$ in the subgraph of $G$ induced by $D \cup \{u,v\}$ is at most $\alpha$ times that in $G$. For general graphs, the only known previous approximability result is an $O(\log n)$-approximation algorithm ($n=|V|$) for $\alpha = 1$ by Ding et al. For any constant $\alpha > 1$, we give an $O(n^{1-\frac{1}{\alpha}}(\log n)^{\frac{1}{\alpha}})$-approximation algorithm. When $\alpha \geq 5$, we give an $O(\sqrt{n}\log n)$-approximation algorithm. Finally, we prove that, when $\alpha =2$, unless $NP \subseteq DTIME(n^{poly\log n})$, for any constant $\epsilon > 0$, the problem admits no polynomial-time $2^{\log^{1-\epsilon}n}$-approximation algorithm, improving upon the $\Omega(\log n)$ bound by Du et al. (albeit under a stronger hardness assumption)

Constraint Generation Algorithm for the Minimum Connectivity Inference Problem

Given a hypergraph $H$, the Minimum Connectivity Inference problem asks for a graph on the same vertex set as $H$ with the minimum number of edges such that the subgraph induced by every hyperedge of $H$ is connected. This problem has received a lot of attention these recent years, both from a theoretical and practical perspective, leading to several implemented approximation, greedy and heuristic algorithms. Concerning exact algorithms, only Mixed Integer Linear Programming (MILP) formulations have been experimented, all representing connectivity constraints by the means of graph flows. In this work, we investigate the efficiency of a constraint generation algorithm, where we iteratively add cut constraints to a simple ILP until a feasible (and optimal) solution is found. It turns out that our method is faster than the previous best flow-based MILP algorithm on random generated instances, which suggests that a constraint generation approach might be also useful for other optimization problems dealing with connectivity constraints. At last, we present the results of an enumeration algorithm for the problem.Comment: 16 pages, 4 tables, 1 figur

Efficiently Correcting Matrix Products

We study the problem of efficiently correcting an erroneous product of two $n\times n$ matrices over a ring. Among other things, we provide a randomized algorithm for correcting a matrix product with at most $k$ erroneous entries running in $\tilde{O}(n^2+kn)$ time and a deterministic $\tilde{O}(kn^2)$-time algorithm for this problem (where the notation $\tilde{O}$ suppresses polylogarithmic terms in $n$ and $k$).Comment: Fixed invalid reference to figure in v

A compact statistical model of the song syntax in Bengalese finch

Songs of many songbird species consist of variable sequences of a finite number of syllables. A common approach for characterizing the syntax of these complex syllable sequences is to use transition probabilities between the syllables. This is equivalent to the Markov model, in which each syllable is associated with one state, and the transition probabilities between the states do not depend on the state transition history. Here we analyze the song syntax in a Bengalese finch. We show that the Markov model fails to capture the statistical properties of the syllable sequences. Instead, a state transition model that accurately describes the statistics of the syllable sequences includes adaptation of the self-transition probabilities when states are repeatedly revisited, and allows associations of more than one state to the same syllable. Such a model does not increase the model complexity significantly. Mathematically, the model is a partially observable Markov model with adaptation (POMMA). The success of the POMMA supports the branching chain network hypothesis of how syntax is controlled within the premotor song nucleus HVC, and suggests that adaptation and many-to-one mapping from neural substrates to syllables are important features of the neural control of complex song syntax

Non-adaptive Group-Testing Aggregate MAC Scheme

This paper applies non-adaptive group testing to aggregate message authentication code (MAC) and introduces non-adaptive group-testing aggregate MAC. After formalization of its syntax and security requirements, simple and generic construction is presented, which can be applied to any aggregate MAC scheme formalized by Katz and Lindell in 2008. Then, two instantioations of the construction is presented. One is based on the aggregate MAC scheme by Katz and Lindell and uses addition for tag aggregate. The other uses cryptographic hashing for tag aggregate. Provable security of the generic construction and two instantiations are also discussed

Seasonal variations in carbon, nitrogen and phosphorus concentrations and C:N:P stoichiometry in different organs of a Larix principis-rupprechtii Mayr. plantation in the Qinling Mountains, China

Understanding how concentrations of elements and their stoichiometry change with plant growth and age is critical for predicting plant community responses to environmental change. Weusedlong-term field experiments to explore how the leaf, stem and root carbon (C), nitrogen (N) and phosphorous (P) concentrations and their stoichiometry changed with growth and stand age in a L.principis-rupprechtii Mayr. plantation from 2012–2015 in the Qinling Mountains, China. Our results showed that the C, N and P concentrations and stoichiometric ratios in different tissues of larch stands were affected by stand age, organ type andsampling month and displayed multiple correlations with increased stand age in different growing seasons. Generally, leaf C and N concentrations were greatest in the fast-growing season, but leaf P concentrations were greatest in the early growing season. However, no clear seasonal tendencies in the stem and root C, N and P concentrations were observed with growth. In contrast to N and P, few differences were found in organ-specific C concentrations. Leaf N:P was greatest in the fast-growing season, while C:N and C:P were greatest in the late-growing season. No clear variations were observed in stem and root C:N, C:P andN:Pthroughout the entire growing season, but leaf N:P was less than 14, suggesting that the growth of larch stands was limited by N in our study region. Compared to global plant element concentrations and stoichiometry, the leaves of larch stands had higher C, P, C:NandC:PbutlowerNandN:P,andtherootshadgreater PandC:NbutlowerN,C:Pand N:P. Our study provides baseline information for describing the changes in nutritional elements with plant growth, which will facilitates plantation forest management and restoration, and makes avaluable contribution to the global data pool on leaf nutrition and stoichiometry

On environment difficulty and discriminating power

The final publication is available at Springer via http://dx.doi.org/10.1007/s10458-014-9257-1This paper presents a way to estimate the difficulty and discriminating power of any task instance. We focus on a very general setting for tasks: interactive (possibly multiagent) environments where an agent acts upon observations and rewards. Instead of analysing the complexity of the environment, the state space or the actions that are performed by the agent, we analyse the performance of a population of agent policies against the task, leading to a distribution that is examined in terms of policy complexity. This distribution is then sliced by the algorithmic complexity of the policy and analysed through several diagrams and indicators. The notion of environment response curve is also introduced, by inverting the performance results into an ability scale. We apply all these concepts, diagrams and indicators to two illustrative problems: a class of agent-populated elementary cellular automata, showing how the difficulty and discriminating power may vary for several environments, and a multiagent system, where agents can become predators or preys, and may need to coordinate. Finally, we discuss how these tools can be applied to characterise (interactive) tasks and (multi-agent) environments. These characterisations can then be used to get more insight about agent performance and to facilitate the development of adaptive tests for the evaluation of agent abilities.I thank the reviewers for their comments, especially those aiming at a clearer connection with the field of multi-agent systems and the suggestion of better approximations for the calculation of the response curves. The implementation of the elementary cellular automata used in the environments is based on the library 'CellularAutomaton' by John Hughes for R [58]. 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