Xingwu Liu

Classifying rendezvous tasks of arbitrary dimension

The rendezvous is a type of distributed decision tasks including many well-known tasks such as set agreement, simplex agreement, and approximation agreement. An n-dimensional rendezvous task, n>=1, allows n+2 distinct input values, and each execution produces at most n+2 distinct output values. A rendezvous task is said to implement another if an instance of its solution, followed by a protocol based on shared read/write registers, solves the other. The notion of implementation induces a classification of rendezvous tasks of every dimension: two tasks belong to the same class if they implement each other. Previous work on classifying rendezvous tasks only focused on 1-dimensional ones. This paper solves an open problem by presenting the classification of nice rendezvous of arbitrary dimension. An n-dimensional rendezvous task is said to be nice if the qth reduced homology group of its decision space is trivial for q n, and free for q=n. Well-known examples are set agreement, simplex agreement, and approximation agreement. Each n-dimensional rendezvous task is assigned an algebraic signature, which consists of the nth homology group of the decision space, as well as a distinguished element in the group. It is shown that an n-dimensional nice rendezvous task implements another if and only if there is a homomorphism from its signature to that of the other. Hence the computational power of a nice rendezvous task is completely characterized by its signature. In each dimension, there are infinitely many classes of rendezvous tasks, and exactly countable classes of nice ones. A representative is explicitly constructed for each class of nice rendezvous tasks.

An adaptive spanning tree-based data collection scheme in wireless sensor networks

In-network data aggregation is a widely used method for collecting data efficiently in wireless sensor networks (WSNs). The authors focus on how to achieve high aggregation efficiency and prolonging networks’ lifetime. Firstly, this paper proposes an adaptive spanning tree algorithm (AST), which can adaptively build and adjust an aggregation spanning tree. Owing to the strategies of random waiting and alternative father nodes, AST can achieve a relatively balanced spanning tree and flexible tree adjustment. Then a redundant aggregation scheme (RAG) is illustrated. In RAG, interior nodes help to forward data for their sibling nodes and thus provide reliable data transmission for WSN. Finally, the simulations demonstrate that (1) AST can prolong the lifetime and (2) RAG makes a better trade-off between storage and aggregation ratio, comparing to other aggregation schemes.

A Classification of Degenerate Loop Agreement

Loop agreement is a type of distributed decision tasks including many well-known tasks such as set agreement, simplex agreement, and approximation agreement. Because of its elegant combinatorial structure and its important role in the decidability problem of distributed decision tasks, loop agreement has been thoroughly investigated. A classification of loop agreement tasks has been proposed, based on their relative computational power: tasks are in the same class if and only if they can implement each other. However, the classification does not cover such important tasks as consensus, because any loop agreement task allows up to three distinct output values in an execution. So, this paper considers classifying a variation of loop agreement, called degenerate loop agreement, which includes consensus. A degenerate loop agreement task is defined in terms of its decision space and two distinguished vertices in the space. It is shown that there are exactly two equivalence classes of degenerate loop agreement tasks: one represented by the trivial task, and the other by consensus. The classification is totally determined by connectivity of the decision space of a task; if the distinguished points are connected in the space, the task is equivalent to the trivial task, otherwise to consensus.

Variable-Version Lovász Local Lemma: Beyond Shearer's Bound

A tight criterion under which the abstract version Lovász Local Lemma (abstract-LLL) holds was given by Shearer [41] decades ago. However, little is known about that of the variable version LLL (variable-LLL) where events are generated by independent random variables, though variable- LLL naturally models and is enough for almost all applications of LLL. We introduce a necessary and sufficient criterion for variable-LLL, in terms of the probabilities of the events and the event-variable graph specifying the dependency among the events. Based on this new criterion, we obtain boundaries for two families of event-variable graphs, namely, cyclic and treelike bigraphs. These are the first two non-trivial cases where the variable-LLL boundary is fully determined. As a byproduct, we also provide a universal constructive method to find a set of events whose union has the maximum probability, given the probability vector and the event-variable graph.Though it is #P-hard in general to determine variable- LLL boundaries, we can to some extent decide whether a gap exists between a variable-LLL boundary and the corresponding abstract-LLL boundary. In particular, we show that the gap existence can be decided without solving Shearer’s conditions or checking our variable-LLL criterion. Equipped with this powerful theorem, we show that there is no gap if the base graph of the event-variable graph is a tree, while gap appears if the base graph has an induced cycle of length at least 4. The problem is almost completely solved except when the base graph has only 3-cliques, in which case we also get partial solutions.A set of reduction rules are established that facilitate to infer gap existence of a event-variable graph from known ones. As an application, various event-variable graphs, in particular combinatorial ones, are shown to be gapful/gapless.

Detecting Anomaly in Traffic Flow from Road Similarity Analysis

Taxies equipped with GPS devices are considered as 24-hour moving sensors widely distributed in urban road networks. Plenty of accurate and realtime trajectories of taxi are recorded by GPS devices and are commonly studied for understanding traffic dynamics. This paper focuses on anomaly detection in traffic volume, especially the non-recurrent traffic anomaly caused by unexpected or transient incidents, such as traffic accidents, celebrations and disasters. It is important to detect such sharp changes of traffic status for sensing abnormal events and planning their impact on the smooth volume of traffic. Unlike existing anomaly detection approaches that mainly monitor the derivation of current traffic status from history in the past, the proposed method in this paper evaluates the abnormal score of traffic on one road by comparing its current traffic volume with not only its historical data but also its neighbors. We define the neighbors as the roads that are close in sense of both geo-location and traffic patterns, which are extracted by matrix factorization. The evaluation results on trajectories data of 12,286 taxies over four weeks in Beijing show that our approach outperforms other baseline methods with higher precision and recall.

Shortest Paths on Evolving Graphs

We consider the shortest path problem in evolving graphs with restricted access, i.e., the changes are unknown and can be probed only by limited queries. The goal is to maintain a shortest path between a given pair of nodes. We propose a heuristic algorithm that takes into account time-dependent edge reliability and reduces the problem to find an edge-weighted shortest path. Our algorithm leads to higher precision and recall than those of the existing method introduced in [5] on both real-life data and synthetic data, while the error is negligible.

How to Select the Top k Elements from Evolving Data

In this paper we investigate the top-k-selection problem, i.e. to determine and sort the top k elements, in the dynamic data model. Here dynamic means that the underlying total order evolves over time, and that the order can only be probed by pair-wise comparisons. It is assumed that at each time step, only one pair of elements can be compared. This assumption of restricted access is reasonable in the dynamic model, especially for massive data set where it is impossible to access all the data before the next change occurs. Previously only two special cases were studied [1] in this model: selecting the element of a given rank, and sorting all elements. This paper systematically deals with \(k\in [n]\). Specifically, we identify the critical point \(k^*\) such that the top-k-selection problem can be solved error-free with probability \(1-o(1)\) if and only if \(k=o(k^*)\). A lower bound of the error when \(k=\varOmega (k^*)\) is also determined, which actually is tight under some conditions. In contrast, we show that the top-k-set problem, which means finding the top k elements without sorting them, can be solved error-free with probability \(1-o(1)\) for all \(1\le k\le n\). Additionally, we consider some extensions of the dynamic data model and show that most of these results still hold.

A Chemical Interpretation of GSML Programs

GSML is a programming language that has been designed for grid end-users to overcome the programming hurdle and the high learning curve associated with grid infrastructures that are complex distributed computing systems. This paper defines its formal semantics in terms of a chemical programming language called HOCL. This translation of GSML programs into HOCL gives a precise definition of the concepts of GSML, especially sessions. The semantics also bridges the GSML and chemical computing paradigms.

Communities in Preference Networks: Refined Axioms and Beyond

Borgs et al. [2016] investigated essential requirements for communities in preference networks. They defined six axioms on community functions, i.e., community detection rules. Though having elegant properties, the practicality of this axiomsystem is compromised by the intractability of checking twocritical axioms, so no nontrivial consistent community functionwas reported in [Borgs et al., 2016]. By adapting the two axioms in a natural way, we propose two new axioms that are efficiently-checkable. We show that most of the desirable properties of the original axiom system are preserved. More importantly, the new axioms provide a general approach to constructing consistent community functions. We further find a natural consistent community function that is also enumerable and samplable, answering an open problem in the literature.

On the Near-Linear Correlation of the Eigenvalues Across BLOSUM Matrices

The BLOSUM matrices estimate the likelihood for one amino acid to be substituted with another, and are commonly used in sequence alignments. Each BLOSUM matrix is associated with a parameter x—the matrix elements are computed based on the diversity among sequences of no more than x% similar. In an earlier work, Song et al. observed a property in the BLOSUM matrices—eigendecompositions of the matrices produce nearly identical sets of eigenvectors. Furthermore, for each eigenvector, a nearly linear trend is observed in all its eigenvalues. This property allowed Song et al. to devise an iterative alignment and matrix selection process to produce more accurate matrices. In this paper, we investigate the reasons behind this property of the BLOSUM matrices. Using this knowledge, we analyze the situations under which the property holds, and hence clarify the extent of the earlier method’s validity.