Distance-Regular Graphs

Graph layout problems are a particular class of combinatorial optimization problems whose goal is to find a linear layout of an input graph in such way that a certain objective cost is optimized. This survey considers their motivation, complexity, approximation properties, upper and lower bounds, heuristics and probabilistic analysis on random graphs. The result is a complete view of the current state of the art with respect to layout problems from an algorithmic point of view.

A survey of graph layout problems

Content aware resizing gained popularity lately and users can now choose from a battery of methods to retarget their media. However, no single retargeting operator performs well on all images and all target sizes. In a user study we conducted, we found that users prefer to combine seam carving with cropping and scaling to produce results they are satisfied with. This inspires us to propose an algorithm that combines different operators in an optimal manner. We define a resizing space as a conceptual multi-dimensional space combining several resizing operators, and show how a path in this space defines a sequence of operations to retarget media. We define a new image similarity measure, which we term Bi-Directional Warping (BDW), and use it with a dynamic programming algorithm to find an optimal path in the resizing space. In addition, we show a simple and intuitive user interface allowing users to explore the resizing space of various image sizes interactively. Using key-frames and interpolation we also extend our technique to retarget video, providing the flexibility to use the best combination of operators at different times in the sequence.

/pdf/multi-operator-media-retargeting-1bj3gdcmgy.pdf

Multi-operator media retargeting

The problem of estimating relative time (or depth) shifts between two seismic images is ubiquitous in seismic data processing. This problem is especially difficult where shifts are large and vary rapidly with time and space, and where images are contaminated with noise or for other reasons are not shifted versions of one another. A new solution to this problem requires only simple extensions of a classic dynamic time warping algorithm for speech recognition. A key component of that classic algorithm is a nonlinear accumulation of alignment errors. By applying the same nonlinear accumulator repeatedly in all directions along all sampled axes of a multidimensional image, I obtain a new and effective method for dynamic image warping (DIW). In tests where known shifts vary rapidly, this new method is more accurate than methods based on crosscorrelations of windowed images. DIW also aligns seismic reflectors well in examples where shifts are unknown, for images with differences not limited to time shifts.

Dynamic warping of seismic images

We present the application of different nonlinear image deformation models to the task of image recognition The deformation models are especially suited for local changes as they often occur in the presence of image object variability We show that, among the discussed models, there is one approach that combines simplicity of implementation, low-computational complexity, and highly competitive performance across various real-world image recognition tasks We show experimentally that the model performs very well for four different handwritten digit recognition tasks and for the classification of medical images, thus showing high generalization capacity In particular, an error rate of 054 percent on the MNIST benchmark is achieved, as well as the lowest reported error rate, specifically 126 percent, in the 2005 international ImageCLEF evaluation of medical image specifically categorization

/pdf/deformation-models-for-image-recognition-4y6w31onnf.pdf

Deformation Models for Image Recognition

http://www-i6.informatik.rwth-aachen.de/PostScript/InterneArbeiten/Keysers_Elastic_Image_Matching_is_NP_complete_Pattern_Recognition_Letters_2003.pdf

Elastic image matching is NP-complete

Approximation algorithms for the TSP with sharpened triangle inequality

We study the problem of centrally scheduling multiple messages in a linear network, when each message has both a release time and a deadline. We show that the problem of transmitting optimally many messages is NP-hard, both when messages may be buffered in transit and when they may not be; for either case, we present efficient algorithms that produce approximately optimal schedules. In particular, our bufferless scheduling algorithm achieves throughput that is within a factor of two of optimal. We show that buffering can improve throughput in general by a logarithmic factor (but no more), but that in several significant special cases, such as when all messages can be released immediately, buffering can help by only a small constant factor. Finally, we show how to convert our centralized, offline bufferless schedules to equally productive fully * Email: micah@cs. toronto edu. Supported by an operating grant from the Natural Sciences and Engineering Research Council of Canada, and by ITRC, an Ontario Centre of Excellence. Thts research was conducted in part while he was at the Heinz Nixdorf Institute Graduate College, D-33095 Paderborn, Germany. ’ Email: rsnbrg@cs .umass edu. Supported in pan by NSF Grant CCR-9710367. t Email: ramesh@cs umass edu. Supported in part by an NSF CAREER Award No. CCR-97-03017. A portion of the research of the second and third author was done while visiting the Dept. of Mathematics and Infotmatik, Univ. of Paderhorn, Paderbom, Germany. 5 Emal: quacksOil.informatik.rwth-aachen.de The work was carried out white the author was a member of the research group of B. Monien at the University of Paderbom. This work and the visits of the second and third author was partially supported by the German Research Association (DFG) within the SFB 376 “Massive Parallelit%t: Algorithmen, Entwurfsmethoden, Anwendungen”. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the fti page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission an&or a fee. SPAA 98 Puerto Vallarta Mexico Copyright ACM 1998 O-89791-989-0/98/ 6...$5.00 Arnold L. Rosenberg+ Dept. of Computer Science, Univ. of Massachusetts, Amherst, MA 01003 Walter Unger§ Lehrstuhl fur Informatik I, RWTH Aachen, Ahomstr. 55, 52074 Aachen, Germany distributed online buffered ones. Most of our results extend readily to ring-structured networks. 1 The Time-Constrained Communication Problem

/pdf/scheduling-time-constrained-communication-in-linear-networks-32qk7sq7yb.pdf

Scheduling time-constrained communication in linear networks

The one sided crossing minimization problem consists of placing the vertices of one part of a bipartite graph on prescribed positions on a straight line and finding the positions of the vertices of the second part on a parallel line and drawing the edges as straight lines such that the number of pairwise edge crossings is minimized. This problem represents the basic building block used for drawing hierarchical graphs aesthetically or producing row-based VLSI layouts. Eades and Wormald [3] showed that the problem is NP-hard for dense graphs. Typical graphs of practical interest are usually very sparse. We prove that the problem remains NP-hard even for forests of 4-stars.

/pdf/one-sided-crossing-minimization-is-np-hard-for-sparse-graphs-3xhya3a8yy.pdf

One Sided Crossing Minimization Is NP-Hard for Sparse Graphs

We study online algorithms with advice for the problem of coloring graphs which come as input vertex by vertex. We consider the class of all 3-colorable graphs and its sub-classes of chordal and maximal outerplanar graphs, respectively.

/pdf/advice-complexity-of-the-online-coloring-problem-4smbkocp2c.pdf

Walter Unger

Papers

Elastic image matching is NP-complete

Approximation algorithms for the TSP with sharpened triangle inequality

Scheduling time-constrained communication in linear networks

One Sided Crossing Minimization Is NP-Hard for Sparse Graphs

Advice Complexity of the Online Coloring Problem