Christian Sommer

Bio: Christian Sommer is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Planar graph & Shortest path problem. The author has an hindex of 17, co-authored 43 publications receiving 1042 citations. Previous affiliations of Christian Sommer include ETH Zurich & National Institute of Informatics.

Shortest-path queries in static networks

Abstract: We consider the point-to-point (approximate) shortest-path query problem, which is the following generalization of the classical single-source (SSSP) and all-pairs shortest-path (APSP) problems: we are first presented with a network (graph). A so-called preprocessing algorithm may compute certain information (a data structure or index) to prepare for the next phase. After this preprocessing step, applications may ask shortest-path or distance queries, which should be answered as fast as possible.Due to its many applications in areas such as transportation, networking, and social science, this problem has been considered by researchers from various communities (sometimes under different names): algorithm engineers construct fast route planning methods; database and information systems researchers investigate materialization tradeoffs, query processing on spatial networks, and reachability queries; and theoretical computer scientists analyze distance oracles and sparse spanners. Related problems are considered for compact routing and distance labeling schemes in networking and distributed computing and for metric embeddings in geometry as well.In this survey, we review selected approaches, algorithms, and results on shortest-path queries from these fields, with the main focus lying on the tradeoff between the index size and the query time. We survey methods for general graphs as well as specialized methods for restricted graph classes, in particular for those classes with arguable practical significance such as planar graphs and complex networks.

Shortest-path queries for complex networks: exploiting low tree-width outside the core

Abstract: We present new and improved methods for efficient shortest-path query processing. Our methods are tailored to work for two specific classes of graphs: graphs with small tree-width and complex networks. Seemingly unrelated at first glance, these two classes of graphs have some commonalities: complex networks are known to have a core--fringe structure with a dense core and a tree-like fringe.Our main contributions are efficient algorithms and data structures on three different levels. First, we provide two new methods for graphs with small but not necessarily constant tree-width. Our methods achieve new tradeoffs between space and query time. Second, we present an improved tree-decomposition-based method for complex networks, utilizing the methods for graphs with small tree-width. Third, we extend our method to handle the highly inter-connected core with existing exact and approximate methods.We evaluate our algorithms both analytically and experimentally. We prove that our algorithms for low-tree-width graphs achieve improved tradeoffs between space and query time. Our experiments on several real-world complex networks further confirm the efficiency of our methods: Both the exact and the hybrid method have faster preprocessing and query times than existing methods. The hybrid method in particular provides an improved tradeoff between space and accuracy.

Distance Oracles for Sparse Graphs

Abstract: Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer k, they showed an efficient algorithm to construct an approximate distance oracle using space O(kn^{1+1/k}) that can answer queries in time O(k) with a distance estimate that is at most 2k-1 times larger than the actual shortest distance (this ratio is called the stretch).They proved that, under a combinatorial conjecture, their data structure is optimal in terms of space: if a stretch of at most 2k-1 is desired, then the space complexity is at least n^{1+1/k}. Their proof holds even if infinite query time is allowed: it is essentially an "incompressibility" result. Also, the proof only holds for dense graphs, and the best bound it can prove only implies that the size of the data structure is lower bounded by the number of edges of the graph. Naturally, the following question arises: what happens for sparse graphs? In this paper we give a new lower bound for approximate distance oracles in the cell-probe model. This lower bound holds even for sparse (polylog(n)-degree) graphs, and it is not an "incompressibility" bound: we prove a three-way tradeoff between space, stretch, and query time. We show that when the query time is t and the stretch is a, then the space S must be at least n^{1+1/Omega(a*t)} / lg n. This lower bound follows by a reduction from lopsided set disjointness to distance oracles, based on and motivated by recent work of Patrascu. Our results in fact show that for any high-girth regular graph, an approximate distance oracle that supports efficient queries for all subgraphs of G must obey this tradeoff. We also prove some lemmas that count sets of paths in high-girth regular graphs and high-girth regular expanders, which might be of independent interest.

Structured recursive separator decompositions for planar graphs in linear time

Abstract: Given a triangulated planar graph G on n vertices and an integer r

Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs

Abstract: A (1+e)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and preprocessing time. There are strong distance-oracle constructions known for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs (Abraham and Gavoille, PODC'06). However, these require Ω(e-1n lg n) space for n-node graphs. In this paper, for planar graphs, bounded-genus graphs, and minor-excluded graphs we give distance-oracle constructions that require only O(n) space. The big O hides only a fixed constant, independent of e and independent of genus or size of an excluded minor. The preprocessing times for our distance oracle are also faster than those for the previously known constructions. For planar graphs, the preprocessing time is O(nlg2 n). However, our constructions have slower query times. For planar graphs, the query time is O(e-2 lg2 n). For all our linear-space results, we can in fact ensure, for any δ > 0, that the space required is only 1 + δ times the space required just to represent the graph itself.

An overview of AspectJ

Abstract: Aspect] is a simple and practical aspect-oriented extension to Java With just a few new constructs, AspectJ provides support for modular implementation of a range of crosscutting concerns. In AspectJ's dynamic join point model, join points are well-defined points in the execution of the program; pointcuts are collections of join points; advice are special method-like constructs that can be attached to pointcuts; and aspects are modular units of crosscutting implementation, comprising pointcuts, advice, and ordinary Java member declarations. AspectJ code is compiled into standard Java bytecode. Simple extensions to existing Java development environments make it possible to browse the crosscutting structure of aspects in the same kind of way as one browses the inheritance structure of classes. Several examples show that AspectJ is powerful, and that programs written using it are easy to understand.

The Web of Human Sexual Contacts

Abstract: Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.

Route Planning in Transportation Networks

Abstract: We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.

Operating Systems: Design and Implementation

Abstract: Table of Contents CHAPTER 1 INTRODUCTION 1.1 WHAT IS AN OPERATING SYSTEM? 1.2 HISTORY OF OPERATING SYSTEMS 1.3 OPERATING SYSTEM CONCEPTS 1.4 SYSTEM CALLS 1.5 OPERATING SYSTEM STRUCTURE 1.6 OUTLINE OF THE REST OF THIS BOOK 1.7 SUMMARY CHAPTER 2 PROCESSES 2.1 INTRODUCTION TO PROCESSES 2.2 INTERPROCESS COMMUNICATION 2.3 CLASSICAL IPC PROBLEMS 2.4 SCHEDULING 2.5 OVERVIEW OF PROCESSES IN MINIX 3 2.6 IMPLEMENTATION OF PROCESSES IN MINIX 3 2.7 THE SYSTEM TASK IN MINIX 3 2.8 THE CLOCK TASK IN MINIX 3 2.9 SUMMARY CHAPTER 3 INPUT/OUTPUT 3.1 PRINCIPLES OF I/O HARDWARE 3.2 PRINCIPLES OF I/O SOFTWARE 3.3 DEADLOCKS 3.4 OVERVIEW OF I/O IN MINIX 3 3.5 BLOCK DEVICES IN MINIX 3 3.6 RAM DISKS 3.7 DISKS 3.8 TERMINALS 3.9 SUMMARY CHAPTER 4 MEMORY MANAGEMENT 4.1 BASIC MEMORY MANAGEMENT 4.2 SWAPPING 4.3 VIRTUAL MEMORY 4.4 PAGE REPLACEMENT ALGORITHMS 4.5 DESIGN ISSUES FOR PAGING SYSTEMS 4.6 SEGMENTATION 4.7 OVERVIEW OF THE MINIX 3 PROCESS MANAGER 4.8 IMPLEMENTATION OF THE MINIX 3 PROCESS MANAGER 4.9 SUMMARY CHAPTER 5 FILE SYSTEMS 5.1 FILES 5.2 DIRECTORIES 5.3 FILE SYSTEM IMPLEMENTATION 5.4 SECURITY 5.5 PROTECTION MECHANISMS 5.6 OVERVIEW OF THE MINIX 3 FILE SYSTEM 5.7 IMPLEMENTATION OF THE MINIX 3 FILE SYSTEM 5.8 SUMMARY CHAPTER 6 READING LIST AND BIBLIOGRAPHY 6.1 SUGGESTIONS FOR FURTHER READING 6.2 ALPHABETICAL BIBLIOGRAPHY APPENDIX A - INSTALLING MINIX 3 APPENDIX B - MINIX 3 SOURCE CODE LISTING APPENDIX C - INDEX TO FILES INDEX