Consider the execution of a failing program as a sequence of program states. Each state induces the following state, up to the failure. Which variables and values of a program state are relevant for the failure? We show how the Delta Debugging algorithm isolates the relevant variables and values by systematically narrowing the state difference between a passing run and a failing run---by assessing the outcome of altered executions to determine wether a change in the program state makes a difference in the test outcome. Applying Delta Debugging to multiple states of the program automatically reveals the cause-effect chain of the failure---that is, the variables and values that caused the failure.

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Contents 1 Introduction 2 1.1 Notations and Definitions . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Problem Formulations 4 2.1 Integer Programming Formulations . . . . . . . . . . . . . . . . . . . 5 2.2 Continuous Formulations . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Computational Complexity 12 4 Bounds and Estimates 15 5 Exact Algorithms 19 5.1 Enumerative Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.2 Exact Algorithms for the Unweighted Case . . . . . . . . . . . . . . 21 5.3 Exact Algorithms for the Weighted Case . . . . . . . . . . . . . . . . 25 6 Heuristics 27 6.1 Sequential Greedy Heuristics . . . . . . . . . . . . . . . . . . . . . . 28 6.2 Local Search Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . 29 6.3 Advanced Search Heuristics . . . . . . . . . . . . . . . . . . . . . . . 30 6.3.1 Simulated annealing . . . . . . . . . . . . . . . . . . . . . . . 30 6.3.2 Neural networks . . . . . . . . . . . . . . . . . . . . . . . .

Modern search engines answer keyword-based queries extremely efficiently. The impressive speed is due to clever inverted index structures, caching, a domain-independent knowledge of strings, and thousands of machines. Several research efforts have attempted to generalize keyword search to keytree and keygraph searching, because trees and graphs have many applications in next-generation database systems. This paper surveys both algorithms and applications, giving some emphasis to our own work.

Abstract. Programs often have a lot of duplicated code, which makes both understanding and maintenance more difficult. This problem can be alleviated by detecting duplicated code, extracting it into a separate new procedure, and replacing all the clones (the instances of the duplicated code) by calls to the new procedure. This paper describes the design and initial implementation of a tool that finds clones and displays them to the programmer. The novel aspect of our approach is the use of program dependence graphs (PDGs) and program slicing to find isomorphic PDG subgraphs that represent clones. The key benefits of this approach are that our tool can find non-contiguous clones (clones whose components do not occur as contiguous text in the program), clones in which matching statements have been reordered, and clones that are intertwined with each other. Furthermore, the clones that are found are likely to be meaningful computations, and thus good candidates for extraction. 1

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This thesis addresses the issues of scale for practical implementations of simultaneous localisation and mapping (SLAM) in extensive outdoor environments. Building an incremental map while also using it for localisation is of prime importance for mobile robot navigation but, until recently, has been confined to small-scale, mostly indoor, environments. The critical problems for large-scale implementations are as follows. First, data association--- finding correspondences between map landmarks and robot sensor measurements---becomes difficult in complex, cluttered environments, especially if the robot location is uncertain. Second, the information required to maintain a consistent map using traditional methods imposes a prohibitive computational burden as the map increases in size. And third, the mathematics for SLAM relies on assumptions of small errors and near-linearity, and these become invalid for larger maps.

We present a new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the so-called replicator equations—a class of straightforward continuous- and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate mean-field annealing heuristics.

To understand the dynamics of a running program, it is often useful to examine its state at specific moments during its execution. We present memory graphs as a means to capture and explore program states. A memory graph gives a comprehensive view of all data structures of a program; data items are related by operations like dereferencing, indexing or member access. Although memory graphs are typically too large to be visualized as a whole, one can easily focus on specific aspects using well-known graph operations. For instance, a greatest common subgraph visualizes commonalities and differences between program states.

Data association is the process of relating features observed in the environment to features viewed previously or to features in a map. Correct feature association is essential for mobile robot navigation as it allows the robot to determine its location relative to the features it observes. This paper presents a graph theoretic method that is applicable to data association problems where the features are observed via a batch process. Batch observations (e.g., scanning laser, radar, video) detect a set of features simultaneously or with sufficiently small temporal difference that, with motion compensation, the features can be represented with precise relative coordinates. This data association method is described in the context of two possible navigation applications: metric map building with simultaneous localisation, and topological map based localisation. Experimental results are presented using an indoor mobile robot with a 2D scanning laser sensor. Given two scans from different unknown locations, the features common to both scans are mapped to each other and the relative change in pose (position and orientation) of the vehicle between the two scans is obtained. 1