This paper considers the problem of routing connections in a reconfigurable optical network using wavelength division multiplexing, where each connection between a pair of nodes in the network is assigned a path through the network and a wavelength on that path, such that connections whose paths share a common link in the network are assigned different wavelengths. We derive an upper bound on the carried traffic of connections (or equivalently, a lower bound on the blocking probability) for any routing and wavelength assignment (RWA) algorithm in such a network. The bound scales with the number of wavelengths and is achieved asymptotically (when a large number of wavelengths is available) by a fixed RWA algorithm. Although computationally intensive, our bound can be used as a metric against which the performance of different RWA algorithms can be compared for networks of moderate size. We illustrate this by comparing the performance of a simple shortest-path RWA (SP-RWA) algorithm via...

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.

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 . . . . . . . . . . . . . . . . . . . . . . . .

This article investigate different aspects regarding pairwise and multiple structure comparison, and the problem of automatically discover common patterns in a set of structures. Descriptions and representation of structures and patterns are investigated, as well as scoring and algorithms for comparison and discovery. A framework and nomenclature is developed, and a lot of methods are reviewed and placed into this framework.

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.

Abstract—In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on small instances, Gusfield’s IP can be of exponential size in the worst case. Several authors [2], [3] have presented polynomial-sized IPs for the problem. In this paper, we further the work on IP approaches to HIPP. We extend the existing polynomial-sized IPs by introducing several classes of valid cuts for the IP. We also present a new polynomial-sized IP formulation that is a hybrid between two existing IP formulations and inherits many of the strengths of both. Many problems that are too complex for the exponential-sized formulations can still be solved in our new formulation in a reasonable amount of time. We provide a detailed empirical comparison of these IP formulations on both simulated and real genotype sequences. Our formulation can also be extended in a variety of ways to allow errors in the input or model the structure of the population under consideration. Index Terms—Computations on discrete structures, integer programming, biology and genetics, haplotype inference. 1

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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

A complex relation is any n-ary relation in which some of the arguments may be be unspecified. We present here a simple two-stage method for extracting complex relations between named entities in text. The first stage creates a graph from pairs of entities that are likely to be related, and the second stage scores maximal cliques in that graph as potential complex relation instances. We evaluate the new method against a standard baseline for extracting genomic variation relations from biomedical text. 1

To cover the edges of a graph with a minimum number of cliques is an NP-complete problem with many applications. The state-of-the-art solving algorithm is a polynomial-time heuristic from the 1970’s. We present an improvement of this heuristic. Our main contribution, however, is the development of efficient and effective polynomial-time data reduction rules that, combined with a search tree algorithm, allow for exact problem solutions in competitive time. This is confirmed by experiments with real-world and synthetic data. Moreover, we prove the fixed-parameter tractability of covering edges by cliques. 1