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Shortest Paths (shortest + paths)

Distribution by Scientific Domains

Information Science and Computing	25%

Selected Abstracts

Shortest paths in fuzzy weighted graphs

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 11 2004
Chris Cornelis
The task of finding shortest paths in weighted graphs is one of the archetypical problems encountered in the domain of combinatorial optimization and has been studied intensively over the past five decades. More recently, fuzzy weighted graphs, along with generalizations of algorithms for finding optimal paths within them, have emerged as an adequate modeling tool for prohibitively complex and/or inherently imprecise systems. We review and formalize these algorithms, paying special attention to the ranking methods used for path comparison. We show which criteria must be met for algorithm correctness and present an efficient method, based on defuzzification of fuzzy weights, for finding optimal paths. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1051,1068, 2004. [source]

Shortest paths on dynamic graphs

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2008
Giacomo Nannicini
Abstract Among the variants of the well-known shortest path problem, those that refer to dynamically changing graphs are theoretically interesting, as well as computationally challenging. Application-wise, there is an industrial need for computing point-to-point shortest paths on large-scale road networks whose arcs are weighted with a travelling time that depends on traffic conditions. We survey recent techniques for dynamic graph weights as well as dynamic graph topology. [source]

On the complexity of finding paths in a two-dimensional domain I: Shortest paths

MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 6 2004
Arthur W. Chou
Abstract The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: (A) domains with polynomialtime computable boundaries, and (B) polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type (A) and type (B); and it has a polynomial-space lower bound for the domains of type (B), and has a #P lower bound for the domains of type (A). (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Distributed end-host multicast algorithms for the Knowledge Grid

CONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 15 2007
Wanqing Tu
Abstract The Knowledge Grid built on top of the peer-to-peer (P2P) network has been studied to implement scalable, available and sematic-based querying. In order to improve the efficiency and scalability of querying, this paper studies the problem of multicasting queries in the Knowledge Grid. An m -dimensional irregular mesh is a popular overlay topology of P2P networks. We present a set of novel distributed algorithms on top of an m -dimensional irregular mesh overlay for the short delay and low network resource consumption end-host multicast services. Our end-host multicast fully utilizes the advantages of an m -dimensional mesh to construct a two-layer architecture. Compared to previous approaches, the novelty and contribution here are: (1) cluster formation that partitions the group members into clusters in the lower layer where cluster consists of a small number of members; (2) cluster core selection that searches a core with the minimum sum of overlay hops to all other cluster members for each cluster; (3) weighted shortest path tree construction that guarantees the minimum number of shortest paths to be occupied by the multicast traffic; (4) distributed multicast routing that directs the multicast messages to be efficiently distributed along the two-layer multicast architecture in parallel, without a global control; the routing scheme enables the packets to be transmitted to the remote end hosts within short delays through some common shortest paths; and (5) multicast path maintenance that restores the normal communication once the membership alteration appears. Simulation results show that our end-host multicast can distributively achieve a shorter delay and lower network resource consumption multicast services as compared with some well-known end-host multicast systems. Copyright © 2006 John Wiley & Sons, Ltd. [source]

An efficient pursuit automata approach for estimating stable all-pairs shortest paths in stochastic network environments,

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 4 2009
Sudip Misra
Abstract This paper presents a new solution to the dynamic all-pairs shortest-path routing problem using a fast-converging pursuit automata learning approach. The particular instance of the problem that we have investigated concerns finding the all-pairs shortest paths in a stochastic graph, where there are continuous probabilistically based updates in edge-weights. We present the details of the algorithm with an illustrative example. The algorithm can be used to find the all-pairs shortest paths for the ,statistical' average graph, and the solution converges irrespective of whether there are new changes in edge-weights or not. On the other hand, the existing popular algorithms will fail to exhibit such a behavior and would recalculate the affected all-pairs shortest paths after each edge-weight update. There are two important contributions of the proposed algorithm. The first contribution is that not all the edges in a stochastic graph are probed and, even if they are, they are not all probed equally often. Indeed, the algorithm attempts to almost always probe only those edges that will be included in the final list involving all pairs of nodes in the graph, while probing the other edges minimally. This increases the performance of the proposed algorithm. The second contribution is designing a data structure, the elements of which represent the probability that a particular edge in the graph lies in the shortest path between a pair of nodes in the graph. All the algorithms were tested in environments where edge-weights change stochastically, and where the graph topologies undergo multiple simultaneous edge-weight updates. Its superiority in terms of the average number of processed nodes, scanned edges and the time per update operation, when compared with the existing algorithms, was experimentally established. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Priority-based adaptive routing in NGEO satellite networks

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 3 2007
Ömer Korçak
Abstract In a non-geostationary satellite constellation with inter satellite links (ISLs), there could be many shortest paths between two satellites in terms of hop count. An efficient routing algorithm should effectively use these paths in order to distribute traffic to ISLs in a balanced way and to improve the performance of the system. This paper presents and evaluates a novel priority-based adaptive shortest path routing (PAR) scheme in order to achieve this goal. PAR sets the path towards the destination in a distributed manner, using a priority mechanism depending on the past utilization and buffering information of the ISLs. Moreover, to avoid unnecessary splitting of a flow and to achieve better utilization of ISLs, enhanced PAR (ePAR) scheme is proposed. This paper evaluates performance of the proposed techniques by employing an extensive set of simulations. Furthermore, since there are a number of ePAR parameters that should be adjusted depending on the network and traffic characteristics, a detailed analysis of ePAR scheme is provided to form a framework for setting the parameters. This paper also includes a method for adaptation of the proposed algorithms to minimum-delay path routing. Copyright © 2006 John Wiley & Sons, Ltd. [source]

GPSPA: a new adaptive algorithm for maintaining shortest path routing trees in stochastic networks

INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 10 2004
Sudip Misra
Abstract This paper presents a new efficient solution to the Dynamic Shortest Path Routing Problem, using the principles of Generalized Pursuit Learning. It proposes an efficient algorithm for maintaining shortest path routing trees in networks that undergo stochastic updates in their structure. It involves finding the shortest path in a stochastic network, where there are continuous probabilistically based updates in link-costs. In vast, rapidly changing telecommunications (wired or wireless) networks, where links go up and down continuously and rapidly, and where there are simultaneous random updates in link costs, the existing algorithms are inefficient. In such cases, shortest paths need to be computed within a very short time (often in the order of microseconds) by scanning and processing the minimal number of nodes and links. The proposed algorithm, referred to as the Generalized Pursuit Shortest Path Algorithm (GPSPA), will be very useful in this regard, because after convergence, it seems to be the best algorithm to-date for this purpose. Indeed, it has the advantage that it can be used to find the shortest path within the ,statistical' average network, which converges irrespective of whether there are new changes in link-costs or not. Existing algorithms are not characterized by such a behaviour inasmuch as they would recalculate the affected shortest paths after each link-cost update. The algorithm has been rigorously evaluated experimentally, and it has been found to be a few orders of magnitude superior to the algorithms available in the literature. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Shortest paths in fuzzy weighted graphs

Shortest paths on dynamic graphs

Parallel Algorithms for Dynamic Shortest Path Problems

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 3 2002
Ismail Chabini
The development of intelligent transportation systems (ITS) and the resulting need for the solution of a variety of dynamic traffic network models and management problems require faster-than-real-time computation of shortest path problems in dynamic networks. Recently, a sequential algorithm was developed to compute shortest paths in discrete time dynamic networks from all nodes and all departure times to one destination node. The algorithm is known as algorithm DOT and has an optimal worst-case running-time complexity. This implies that no algorithm with a better worst-case computational complexity can be discovered. Consequently, in order to derive algorithms to solve all-to-one shortest path problems in dynamic networks, one would need to explore avenues other than the design of sequential solution algorithms only. The use of commercially-available high-performance computing platforms to develop parallel implementations of sequential algorithms is an example of such avenue. This paper reports on the design, implementation, and computational testing of parallel dynamic shortest path algorithms. We develop two shared-memory and two message-passing dynamic shortest path algorithm implementations, which are derived from algorithm DOT using the following parallelization strategies: decomposition by destination and decomposition by transportation network topology. The algorithms are coded using two types of parallel computing environments: a message-passing environment based on the parallel virtual machine (PVM) library and a multi-threading environment based on the SUN Microsystems Multi-Threads (MT) library. We also develop a time-based parallel version of algorithm DOT for the case of minimum time paths in FIFO networks, and a theoretical parallelization of algorithm DOT on an ,ideal' theoretical parallel machine. Performances of the implementations are analyzed and evaluated using large transportation networks, and two types of parallel computing platforms: a distributed network of Unix workstations and a SUN shared-memory machine containing eight processors. Satisfactory speed-ups in the running time of sequential algorithms are achieved, in particular for shared-memory machines. Numerical results indicate that shared-memory computers constitute the most appropriate type of parallel computing platforms for the computation of dynamic shortest paths for real-time ITS applications. [source]

Scale sensitivity of synthetic long-term vegetation time series derived through overlay of short-term field records

JOURNAL OF VEGETATION SCIENCE, Issue 4 2007
Otto Wildi
Abstract Questions: Is change in cover of dominant species driving the velocity of succession or is it species turnover (1)? Is the length of the time-step chosen in sampling affecting our recognition of the long-term rate of change (2)1 Location: 74 permanent plots located in the Swiss National Park, SE Switzerland, ca. 1900 m a.s.l. Methods: We superimpose several time-series from permanent plots to one single series solely based on compositional dissimilarity. As shown earlier (Wildi & Schütz 2000) this results in a synthetic series covering about 400 to 650 yr length. Continuous power transformation of cover-percentage scores is used to test if the dominance or the presence-absence of species is governing secondary succession from pasture to forest. The effect of time step length is tested by sub-samples of the time series. Results: Altering the weight of presence-absence versus dominance of species affects the emerging time frame, while altering time step length is uncritical. Where species turnover is fast, different performance scales yield similar results. When cover change in dominant species prevails, the solutions vary considerably. Ordinations reveal that the synthetic time series seek for shortest paths of the temporal pattern whereas in the real system longer lasting alternatives exist. Conclusions: Superimposing time series differs from the classical space-for-time substitution approach. It is a computation-based method to investigate temporal patterns of hundreds of years fitting between direct monitoring (usually limited to decades) and the analysis of proxy-data (for time spans of thousands of years and more). [source]

Efficiency and fairness of system-optimal routing with user constraints,

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2006
Andreas S. Schulz
Abstract We study the route-guidance system proposed by Jahn, Möhring, Schulz, and Stier-Moses Operations Research 53 (2005), 600,616 from a theoretical perspective. As system-optimal guidance is known to be problematic, this approach computes a traffic pattern that minimizes the total travel time subject to user constraints. These constraints are designed to ensure that routes suggested to users are not much longer than shortest paths for the prevailing network conditions. To calibrate the system, a certain measure,called normal length,must be selected. We show that when this length is defined as the travel time at equilibrium, the resulting traffic assignment is provably efficient and close to fair. To measure efficiency, we compare the output to the best solution without guidance and to user equilibria. To measure unfairness, we compare travel times of different users, and show that they do not differ too much. Inefficient or unfair traffic assignments cause users to travel too long or discourage people from accepting the system; either consequence would jeopardize the potential impact of a route-guidance system. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 48(4), 223,234 2006 [source]

An approximation algorithm for Stackelberg network pricing,

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2005
Sébastien Roch
Abstract We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly NP-hard. We then provide a polynomial time algorithm with a worst-case precision guarantee of , where mT denotes the number of toll arcs. Finally, we show that the approximation is tight with respect to a natural relaxation by constructing a family of instances for which the relaxation gap is reached. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(1), 57,67 2005 [source]

Connectedness of digraphs and graphs under constraints on the conditional diameter

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2005
X. Marcote
Abstract Given a digraph G with minimum degree , and an integer 0, , , ,, consider every pair of vertex subsets V1 and V2 such that both the minimum out-degree of the induced subdigraph G[V1] and the minimum in-degree of G[V2] are at least ,. The conditional diameter D, of G is defined as the maximum of the distances d(V1, V2) between any two such vertex subsets. Clearly, D0 is the standard diameter and D0 , D1 , ··· , D, holds. In this article, we guarantee appropriate lower bounds for the connectivities and superconnectivities of a digraph G when D, , h(,,), h(,,) being a function of the parameter ,,,which is related to the shortest paths in G. As a corollary of these results, we give some constraints of the kind D, , h(,,), which assure that the digraph is maximally connected, maximally edge-connected, superconnected, or edge-superconnected, extending other previous results of the same kind. Similar statements can be obtained for a graph as a direct consequence of those for its associated symmetric digraph. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(2), 80,87 2005 [source]

A polynomial-time algorithm to find shortest paths with recourse

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2003
J. Scott Provan
Abstract The Shortest Path with Recourse Problem involves finding the shortest expected-length paths in a directed network, each of whose arcs have stochastic traversal lengths (or delays) that become known only upon arrival at the tail of that arc. The traveler starts at a given source node and makes routing decisions at each node in such a way that the expected distance to a given sink node is minimized. We develop an extension of Dijkstra's algorithm to solve the version of the problem where arclengths are nonnegative and reset after each arc traversal. All known no-reset versions of the problem are NP-hard. We make a partial extension to the case where negative arclengths are present. © 2003 Wiley Periodicals, Inc. [source]

Superconnected digraphs and graphs with small conditional diameters

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2002
C. Balbuena
Abstract The conditional diameter D, of a digraph G measures how far apart a pair of vertex sets V1 and V2 can be in such a way that the minimum out-degree and the minimum in-degree of the subdigraphs induced by V1 and V2, respectively, are at least ,. Thus, D0 is the standard diameter and D0 , D1 , ··· , D,, where , is the minimum degree. We prove that if D, , 2l , 3, where l is a parameter related to the shortest paths, then G is maximally connected, is superconnected, or has a good superconnectivity, depending only on whether , is equal to ,,/2,, ,(, , 1)/2,, or ,(, , 1)/3,, respectively. In the edge case, it is enough that D, , 2l , 2. The results for graphs are obtained as a corollary of those for digraphs, because, in the undirected case, l = ,(g , 1)/2,, g being the girth. © 2002 Wiley Periodicals, Inc. [source]

Network modules help the identification of key transport routes, signaling pathways in cellular and other networks

ANNALEN DER PHYSIK, Issue 12 2009
R. Palotai
Abstract Complex systems are successfully reduced to interacting elements via the network concept. Transport plays a key role in the survival of networks , for example the specialized signaling cascades of cellular networks filter noise and efficiently adapt the network structure to new stimuli. However, our general understanding of transport mechanisms and signaling pathways in complex systems is yet limited. Here we summarize the key network structures involved in transport, list the solutions available to overloaded systems for relaxing their load and outline a possible method for the computational determination of signaling pathways. We highlight that in addition to hubs, bridges and the network skeleton, the overlapping modular structure is also essential in network transport. Path-lenghts in the module-space of the yeast protein-protein interaction network indicated that module-based paths may cross fewer modular boundaries than shortest paths. Moreover, by locating network elements in the space of overlapping network modules and evaluating their distance in this ,module space', it may be possible to approximate signaling pathways computationally, which, in turn could serve the identification of signaling pathways of complex systems. Our model may be applicable in a wide range of fields including traffic control or drug design. [source]