Papers by Christos Zaroliagis
We give an overview of models and efficient algorithms for optimally solving timetable informatio... more We give an overview of models and efficient algorithms for optimally solving timetable information problems like "given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?" Two main approaches that transform the problems into shortest path problems are reviewed, including issues like the modeling of realistic details (e.g., train transfers) and further optimization criteria (e.g., the number of transfers). An important topic is also multi-criteria optimization, where in general all attractive connections with respect to several criteria shall be determined. Finally, we discuss the performance of the described algorithms, which is crucial for their application in a real system. 1 (c) Springer. This is the author's version (February 2006), the definite one is part of Springer LNCS. as shortest paths are described in detail in Section 3, where first a simplified problem specification is considered. Later on, in Section 4, extensions of the approaches that cover realistic details are outlined. Multi-criteria optimization is discussed in Section 5, and studies investigating the performance of the algorithms described in this paper are summarized in Section 6. We conclude the survey with some final remarks in Section 7.
Electronic Notes in Theoretical Computer Science, 2004
Using a set of geometric containers to speed up shortest path queries in a weighted graph has bee... more Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G = (V, E), we store, for each edge (u, v) ∈ E, the bounding box of all nodes t ∈ V for which a shortest u-t-path starts with (u, v). Shortest path queries can then be answered by Dijkstra's algorithm restricted to edges where the corresponding bounding box contains the target.
Geometric shortest path containers
In this paper, we consider Dijkstra's algorithm for the single source single tar... more In this paper, we consider Dijkstra's algorithm for the single source single target shortest path problem in large sparse graphs. The goal is to reduce the response time for on-line queries by using precomputed information. Due to the size of the graph, preprocessing space requirements can be only linear in the number of nodes. We assume that a layout of the graph is given. In the preprocessing, we determine from this layout a geometric object for each edge containing all nodes that can be reached by a shortest path starting with that edge. Based on these geometric objects, the search space for on-line computation can be reduced signican tly. Shortest path queries can then be answered by Dijkstra's algorithm restricted to edges where the corresponding geometric object contains the target. We present an extensive experimental study comparing the impact of dieren t types of objects. The test data we use are real-world trac networks, the typical eld of application for this scenario. Furthermore, we present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the geometric containers have to be updated. We evaluate the quality and the time for dieren t update strategies that guarantee correct shortest paths. Finally, we present a software framework in C++ to realize the implementations of all of our variants of Dijkstra's algorithm. A basic implementation of the algorithm is rened for each modication and { even more importantly { these modications can be combined in any possible way without loss of eciency . Keyw ords: Graph algorithms
Journal of Experimental Algorithmics, 2005
A fundamental approach in finding efficiently best routes or optimal itineraries in traffic infor... more A fundamental approach in finding efficiently best routes or optimal itineraries in traffic information systems is to reduce the search space (part of graph visited) of the most commonly used shortest path routine (Dijkstra's algorithm) on a suitably defined graph. We investigate reduction of the search space while simultaneously retaining data structures, created during a preprocessing phase, of size linear (i.e., optimal) to the size of the graph. We show that the search space of Dijkstra's algorithm can be significantly reduced by extracting geometric information from a given layout of the graph and by encapsulating precomputed shortest-path information in resulted geometric objects (containers). We present an extensive experimental study comparing the impact of different types of geometric containers using test data from real-world traffic networks. We also present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the geometric containers have to be updated and show that our new methods are two to three times faster than recomputing everything from scratch. Finally, in an appendix, we discuss the software framework that we developed to realize the implementations of all of our variants of Dijkstra's algorithm. Such a framework is not trivial to achieve as our goal was to maintain a common code base that is, at the same time, small, efficient, and flexible, as we wanted to enhance and combine several variants in any possible way.
Dynamic shortest path containers
Electronic Notes in Theoretical Computer Science, 2003
Abstract: Using a set of geometric containers to speed up shortest path queries in a weightedgrap... more Abstract: Using a set of geometric containers to speed up shortest path queries in a weightedgraph has been proven a useful tool for dealing with large sparse graphs. Given alayout of a graph G = (V, E), we store, for each edge (u, v)E, the bounding boxof all nodes tV for which a shortest u-t-path starts with (u, v). Shortest
Algorithm Engineering and Experimentation, 2004
We consider two approaches that model timetable information in public transportation systems as s... more We consider two approaches that model timetable information in public transportation systems as shortestpath problems in weighted graphs. In the time-expanded approach every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the time-dependent approach the graph contains only one node per station. Both approaches have been recently
Proceedings 11th International Parallel Processing Symposium, 1997
We present a parallel priority data structure that improves the running time of certain algorithm... more We present a parallel priority data structure that improves the running time of certain algorithms for problems that lack a fast and work-e cient parallel solution. As a main application, we give a parallel implementation of Dijkstra's algorithm which runs in O(n) time while performing O(m log n) work on a CREW PRAM. This is a logarithmic factor improvement for the running time compared with previous approaches. The main feature of our data structure is that the operations needed in each iteration of Dijkstra's algorithm can be supported in O(1) time.
Enabling Social Navigation on the Web
2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology, 2008
For a place that gathers millions of people the Web seems pretty lonely at times. This is mainly ... more For a place that gathers millions of people the Web seems pretty lonely at times. This is mainly due to the current pre-dominant browsing scenario; that of an individual partici-pating in an autonomous surfing session. We believe that people should be seen as an integral part of ...
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Proceedings of the nineteenth ACM conference on Hypertext and hypermedia - HT '08, 2008
Eighth Mexican International Conference on Current Trends in Computer Science (ENC 2007), 2007
Searchius is a collaborative search engine that produces search results based solely on user prov... more Searchius is a collaborative search engine that produces search results based solely on user provided web-related data. We discuss the architecture of this system and how it compares to current state-of-the-art search engines. We show that the global users' preference over pages can be efficiently used as a metric of page quality, and that the inherent organization of the collected data can be used to discover related URLs. We also conduct an extensive experimental study, based on the web related data of 36483 users, to analyze the qualitative and quantitative characteristics of user collected URL collections, to investigate how well the users URL collections cover the web and discover the characteristics that affect the quality of the search results under the proposed setting.
Optimal parallel shortest paths in small treewidth digraphs
Lecture Notes in Computer Science, 1995
We consider the problem of preprocessing an n-vertex digraph with real edge weights so that subse... more We consider the problem of preprocessing an n-vertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently answered. We give parallel algorithms for the EREW PRAM model of computation that depend on the treewidth of the input graph. When the treewidth is a constant, our algorithms can answer distance queries in O((n)) time using a single processor, after a preprocessing of O(log2 n) time and O(n) work, where (n) is the inverse of Ackermann's function. The class of constant treewidth graphs contains outerplanar graphs and series-parallel graphs, among others. To the best of our knowledge, these are the first parallel algorithms which achieve these bounds for any class of graphs except trees. We also give a dynamic algorithm which, after a change in an edge weight, updates our data structures in O(log n) time using O(n ) work, for any constant 0O(log2 n) time using O(n) work.
Lecture Notes in Computer Science, 1995
We consider the problem of preprocessing an n-vertex digraph with real edge weights so that subse... more We consider the problem of preprocessing an n-vertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently answered. We give algorithms that depend on the treewidth of the input graph. When the treewidth is a constant, our algorithms can answer distance queries in O(α(n)) time after O(n) preprocessing. This improves upon previously known results for the same problem. We also give a dynamic algorithm which, after a change in an edge weight, updates the data structure in time O(n β ), for any constant 0 < β < 1. The above two algorithms are based on an algorithm of independent interest: computing a shortest path tree, or finding a negative cycle in linear time.
Lecture Notes in Computer Science, 2005
During the last years web search engines have moved from the simple but inefficient syntactical a... more During the last years web search engines have moved from the simple but inefficient syntactical analysis (first generation) to the more robust and usable web graph analysis (second generation). Much of the current research is focussed on the so-called third generation search engines that, in principle, inject "human characteristics" on how results are obtained and presented to the end user. Approaches exploited towards this direction include (among others): an alteration of PageRank [1] that takes into account user specific characteristics and bias the page ordering using the user preferences (an approach, though, that does not scale well with the number of users). The approach is further exploited in [3], where several PageRanks are computed for a given number of distinct search topics. A similar idea is used in , where the PageRank computation takes into account the content of the pages and the query terms the surfer is looking for. In [4], a decomposition of PageRank to basic components is suggested that may be able to scale the different PageRank computations to a bigger number of topics or even distinct users. Another approach to web search is presented in [2], where a rich extension of the web, called semantic web, and the application of searching over this new setting is described.
Lecture Notes in Computer Science, 2004
Proceedings of the Twenty-Eighth Hawaii International Conference on System Sciences, 1995
Fast parallel approximations of the maximum weighted cut problem through derandomization
Lecture Notes in Computer Science, 1989
... Weighted Cut Problem through Derandomization* Grammati Pantziou I Paul Spirakis 1,2 Christos ... more ... Weighted Cut Problem through Derandomization* Grammati Pantziou I Paul Spirakis 1,2 Christos Zaroliagis I ... [Alon, Babai, Itai, 86] provide an excellent account of this approach and credit the original ideas to [Joffe, 74] and [Lancaster, 65], also [Bernstein, 45]. ...
Lecture Notes in Computer Science, 1995
We present algorithms for maintaining shortest path information in dynamic outerplanar digraphs w... more We present algorithms for maintaining shortest path information in dynamic outerplanar digraphs with sublogarithmic query time. By choosing appropriate parameters we achieve continuous trade-offs between the preprocessing, query, and update times. Our data structure is based on a recursive separator decomposition of the graph and it encodes the shortest paths between the members of a properly chosen subset of vertices. We apply this result to construct improved shortest path algorithms for dynamic planar digraphs.
Lecture Notes in Computer Science, 1995
We examine the problem of transmitting in minimum time a given amount of data between a source an... more We examine the problem of transmitting in minimum time a given amount of data between a source and a destination in a network with finite channel capacities and non-zero propagation delays. In the absence of delays, the problem has been shown to be solvable in polynomial time. In this paper, we show that the general problem is NP-hard. In addition, we examine transmissions along a single path, called the quickest path, and present algorithms for general and sparse networks that outperform previous approaches. The first dynamic algorithm for the quickest path problem is also given.
Computing shortest paths and distances in planar graphs
Lecture Notes in Computer Science, 1991
We provide here efficient sequential and parallel solutions to the following problem: given a pla... more We provide here efficient sequential and parallel solutions to the following problem: given a planar digraph G (with real edge weights but no negative cycles) for preprocessing, answer on-line queries requesting the shortest distance (or path) between any two vertices in G. Our algorithms for preprocessing need O(n log n + q 2) space and O(n log n + q
Optimal parallel algorithms for sparse graphs
Lecture Notes in Computer Science, 1991
Page 1. Optimal Parallel Algorithms for Grammati E. Pantziou t Paul G. Spirakis 1,2 Sparse Graphs... more Page 1. Optimal Parallel Algorithms for Grammati E. Pantziou t Paul G. Spirakis 1,2 Sparse Graphs* Christos D. Zaroliagis 1 (1) Computer Technology Institute, PO Box 1122, 26110 Patras, Greece Computer Sc and Eng Dept, University of Patras, Greece ...
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Papers by Christos Zaroliagis