Approximating the Minimum Equivalent Digraph

The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives an approximation algorithm with performance guarantee of pi^2/6 ~ 1.64. The algorithm and its analysis are based on the simple idea of contracting long cycles. (This result is strengthened slightly in ``On strongly connected digraphs with bounded cycle length'' (1996).) The analysis applies directly to 2-Exchange, a simple ``local improvement'' algorithm, showing that its performance guarantee is 1.75.Comment: conference version in ACM-SIAM Symposium on Discrete Algorithms (1994

Minimum Equivalent Precedence Relation Systems

In this paper two related simplification problems for systems of linear inequalities describing precedence relation systems are considered. Given a precedence relation system, the first problem seeks a minimum subset of the precedence relations (i.e., inequalities) which has the same solution set as that of the original system. The second problem is the same as the first one except that the ``subset restriction'' in the first problem is removed. This paper establishes that the first problem is NP-hard. However, a sufficient condition is provided under which the first problem is solvable in polynomial-time. In addition, a decomposition of the first problem into independent tractable and intractable subproblems is derived. The second problem is shown to be solvable in polynomial-time, with a full parameterization of all solutions described. The results in this paper generalize those in [Moyles and Thompson 1969, Aho, Garey, and Ullman 1972] for the minimum equivalent graph problem and transitive reduction problem, which are applicable to unweighted directed graphs

The Adversarial Noise Threshold for Distributed Protocols

We consider the problem of implementing distributed protocols, despite adversarial channel errors, on synchronous-messaging networks with arbitrary topology. In our first result we show that any $n$-party $T$-round protocol on an undirected communication network $G$ can be compiled into a robust simulation protocol on a sparse ($\mathcal{O}(n)$ edges) subnetwork so that the simulation tolerates an adversarial error rate of $\Omega\left(\frac{1}{n}\right)$; the simulation has a round complexity of $\mathcal{O}\left(\frac{m \log n}{n} T\right)$, where $m$ is the number of edges in $G$. (So the simulation is work-preserving up to a $\log$ factor.) The adversary's error rate is within a constant factor of optimal. Given the error rate, the round complexity blowup is within a factor of $\mathcal{O}(k \log n)$ of optimal, where $k$ is the edge connectivity of $G$. We also determine that the maximum tolerable error rate on directed communication networks is $\Theta(1/s)$ where $s$ is the number of edges in a minimum equivalent digraph. Next we investigate adversarial per-edge error rates, where the adversary is given an error budget on each edge of the network. We determine the exact limit for tolerable per-edge error rates on an arbitrary directed graph. However, the construction that approaches this limit has exponential round complexity, so we give another compiler, which transforms $T$-round protocols into $\mathcal{O}(mT)$-round simulations, and prove that for polynomial-query black box compilers, the per-edge error rate tolerated by this last compiler is within a constant factor of optimal.Comment: 23 pages, 2 figures. Fixes mistake in theorem 6 and various typo

Automated Change Rule Inference for Distance-Based API Misuse Detection

Developers build on Application Programming Interfaces (APIs) to reuse existing functionalities of code libraries. Despite the benefits of reusing established libraries (e.g., time savings, high quality), developers may diverge from the API's intended usage; potentially causing bugs or, more specifically, API misuses. Recent research focuses on developing techniques to automatically detect API misuses, but many suffer from a high false-positive rate. In this article, we improve on this situation by proposing ChaRLI (Change RuLe Inference), a technique for automatically inferring change rules from developers' fixes of API misuses based on API Usage Graphs (AUGs). By subsequently applying graph-distance algorithms, we use change rules to discriminate API misuses from correct usages. This allows developers to reuse others' fixes of an API misuse at other code locations in the same or another project. We evaluated the ability of change rules to detect API misuses based on three datasets and found that the best mean relative precision (i.e., for testable usages) ranges from 77.1 % to 96.1 % while the mean recall ranges from 0.007 % to 17.7 % for individual change rules. These results underpin that ChaRLI and our misuse detection are helpful complements to existing API misuse detectors

The optimality of syntactic dependency distances

It is often stated that human languages, as other biological systems, are shaped by cost-cutting pressures but, to what extent? Attempts to quantify the degree of optimality of languages by means of an optimality score have been scarce and focused mostly on English. Here we recast the problem of the optimality of the word order of a sentence as an optimization problem on a spatial network where the vertices are words, arcs indicate syntactic dependencies and the space is defined by the linear order of the words in the sentence. We introduce a new score to quantify the cognitive pressure to reduce the distance between linked words in a sentence. The analysis of sentences from 93 languages representing 19 linguistic families reveals that half of languages are optimized to a 70% or more. The score indicates that distances are not significantly reduced in a few languages and confirms two theoretical predictions, i.e. that longer sentences are more optimized and that distances are more likely to be longer than expected by chance in short sentences. We present a new hierarchical ranking of languages by their degree of optimization. The statistical advantages of the new score call for a reevaluation of the evolution of dependency distance over time in languages as well as the relationship between dependency distance and linguistic competence. Finally, the principles behind the design of the score can be extended to develop more powerful normalizations of topological distances or physical distances in more dimensions

An adaptive distributed algorithm for path aggregation.

Zhang, Zhenyi.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 55-[58]).Abstracts in Chinese and English.Chapter 1 --- Introduction --- p.1Chapter 2 --- Problem Formulation --- p.4Chapter 3 --- Examples --- p.7Chapter 3.1 --- Examples of Undirected Graph --- p.7Chapter 3.1.1 --- Example 1: SPF Routing --- p.7Chapter 3.1.2 --- Example 2: rings --- p.7Chapter 3.1.3 --- Example 3: grid --- p.8Chapter 3.1.4 --- Example 4: cube --- p.9Chapter 3.1.5 --- Example 5: random graph X --- p.10Chapter 3.1.6 --- Example 6: random graph Y --- p.10Chapter 3.2 --- An Example for Directive Graph --- p.11Chapter 4 --- The Framework --- p.13Chapter 4.1 --- The distributed algorithm --- p.13Chapter 4.2 --- The modules --- p.14Chapter 4.3 --- Path control --- p.15Chapter 4.4 --- The forwarding module --- p.18Chapter 4.5 --- The routing module --- p.19Chapter 4.5.1 --- Non-weighted Routing (NWR) --- p.19Chapter 4.5.2 --- Weighted Routing (WR) --- p.20Chapter 4.6 --- Packet Aggregation (PKA) --- p.21Chapter 5 --- Experiments of Path Aggregation --- p.23Chapter 5.1 --- System Setup --- p.24Chapter 5.2 --- Experiment Results --- p.25Chapter 6 --- Convergence --- p.28Chapter 6.1 --- Simulation study --- p.34Chapter 6.2 --- Optimality --- p.34Chapter 6.3 --- Speed of Convergence --- p.37Chapter 7 --- The adaptive property --- p.41Chapter 7.1 --- Adapting to new links --- p.42Chapter 7.2 --- Adapting to topology changing --- p.43Chapter 7.3 --- Adapting to interference and congestion --- p.45Chapter 7.4 --- Adapting to traffic flows --- p.45Chapter 7.5 --- Adapting to capacity --- p.46Chapter 8 --- Related works --- p.48Chapter 8.1 --- Spanning Tree --- p.48Chapter 8.2 --- Minimum Equivalent Directed Graph Problem --- p.49Chapter 8.3 --- Topology Control --- p.50Chapter 8.4 --- The Relationship with our problem --- p.53Chapter 9 --- Conclusion --- p.5