Parameterized Rural Postman Problem

The Directed Rural Postman Problem (DRPP) can be formulated as follows: given a strongly connected directed multigraph $D=(V,A)$ with nonnegative integral weights on the arcs, a subset $R$ of $A$ and a nonnegative integer $\ell$, decide whether $D$ has a closed directed walk containing every arc of $R$ and of total weight at most $\ell$. Let $k$ be the number of weakly connected components in the the subgraph of $D$ induced by $R$. Sorge et al. (2012) ask whether the DRPP is fixed-parameter tractable (FPT) when parameterized by $k$, i.e., whether there is an algorithm of running time $O^*(f(k))$ where $f$ is a function of $k$ only and the $O^*$ notation suppresses polynomial factors. Sorge et al. (2012) note that this question is of significant practical relevance and has been open for more than thirty years. Using an algebraic approach, we prove that DRPP has a randomized algorithm of running time $O^*(2^k)$ when $\ell$ is bounded by a polynomial in the number of vertices in $D$. We also show that the same result holds for the undirected version of DRPP, where $D$ is a connected undirected multigraph

Parameterized Directed kk-Chinese Postman Problem and kk Arc-Disjoint Cycles Problem on Euler Digraphs

In the Directed $k$-Chinese Postman Problem ($k$-DCPP), we are given a connected weighted digraph $G$ and asked to find $k$ non-empty closed directed walks covering all arcs of $G$ such that the total weight of the walks is minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513 (2013) 124--128) asked for the parameterized complexity of $k$-DCPP when $k$ is the parameter. We prove that the $k$-DCPP is fixed-parameter tractable. We also consider a related problem of finding $k$ arc-disjoint directed cycles in an Euler digraph, parameterized by $k$. Slivkins (ESA 2003) showed that this problem is W[1]-hard for general digraphs. Generalizing another result by Slivkins, we prove that the problem is fixed-parameter tractable for Euler digraphs. The corresponding problem on vertex-disjoint cycles in Euler digraphs remains W[1]-hard even for Euler digraphs

Approximation Algorithms for Mixed, Windy, and Capacitated Arc Routing Problems

We show that any alpha(n)-approximation algorithm for the n-vertex metric asymmetric Traveling Salesperson problem yields O(alpha(C))-approximation algorithms for various mixed, windy, and capacitated arc routing problems. Herein, C is the number of weakly-connected components in the subgraph induced by the positive-demand arcs, a number that can be expected to be small in applications. In conjunction with known results, we derive constant-factor approximations if C is in O(log n) and O(log(C)/log(log(C)))-approximations in general

Generating synchronizable test sequences with overlaps

Finite-state-machine-based conformance testing has been comprehensively studied in the literature in the context of centralized test architecture. As distributed test architecture involves multiple remote testers, applying a test sequence generated from a given n-port finite state machine to an implementation under test (IUT) may result in controllability problems. A possible way to resolve this problem is to select an appropriate test sequence, whose application to the IUT will not involve controllability problems. Thus generating such efficient test sequences is an interesting issue. There are several possibilities for such test sequence generation and we provide empirical study to compare the efficiency of two typical solutions proposed in the literature in terms of the length of the generated test sequences. While both of the two techniques rely on solutions to the Rural Postman Problem (RPP), a well-used RPP solution has been adopted and further improved in this thesis work

A Constraint-Solving Approach for Achieving Minimal-Reset Transition Coverage of Smartcard Behaviour

Smartcards are security critical devices requiring a high assurance verification approach. Although formal techniques can be used at design or even at development stages, such systems have to undergo a traditional hardware-in-the-loop testing phase. This phase is subject to two key requirements: achieving exhaustive transition coverage of the behavior of the system under test, and minimizing the testing time. In this context, testing time is highly bound to a specific hardware reset operation. Model-based testing is the adequate approach given the availability of a precise model of the system behavior and its ability to produce high quality coverage while optimizing some cost criterion. %l'argument n'est pas convainquant.This paper presents an original algorithm addressing this problem by reformulating it as an integer programming problem to make a graph Eulerian. The associated cost criterion captures both the number of resets and the total length of the test suite, as an auxiliary objective. The algorithm ensures transition coverage. An implementation of the algorithm was developed, benchmarked, and integrated into an industrial smartcard testing framework. A validation case study from this domain is also presented. The approach can of course be applied to any other domains with similar reset-related testing constraints

An updated annotated bibliography on arc routing problems

The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post-disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising.info:eu-repo/semantics/publishedVersio