Finding the k shortest paths

Eppstein, David

doi:10.1109/sfcs.1994.365697

Cited by 446 publications

(472 citation statements)

References 52 publications

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“…However, every time we add a path, we need to test whether or not this path creates new paths of length greater than τ . To this end, we can use one of the algorithms in the literature of graph theory (e.g., [Eppstein 1999]) to find and add the k shortest paths in an ordinary weighted digraph.…”

Section: Adding a Single Bounded-time Leads-to Propertymentioning

confidence: 99%

Revising UNITY Programs: Possibilities and Limitations

Ebnenasir

Kulkarni

Bonakdarpour

2006

Lecture Notes in Computer Science

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We concentrate on automatic addition of untimed and real-time UNITY properties to programs by local redesign. The main focus of this paper is to identify instances where addition of UNITY properties can be achieved efficiently (in polynomial time) and where the problem of adding UNITY properties is difficult (NP-complete).Regarding addition of UNITY properties in polynomial time, we present a sound and complete algorithm that adds a single leads-to property (respectively, bounded-time leads-to property) and a conjunction of unless, stable, and invariant properties (respectively, bounded-time unless and stable) to an existing untimed (respectively, real-time) UNITY program. Since ensures can be expressed as a conjunction of a leads-to and unless, our algorithms can also be used to add one ensures property along with a conjunction of safety properties.Regarding hardness results, we show that (1) while one leads-to (respectively, ensures) property can be added in polynomial time, the problem of adding two such properties (or any combination of leads-to and ensures) is NP-complete, (2) if maximum non-determinism is desired then the problem of adding even a single leads-to property is NP-complete, and (3) the problem of providing maximum non-determinism while adding a single bounded-time leads-to property to a real-time program is NP-complete (in the size of the time-abstract bisimulation representation of the program) even if the original program satisfies the corresponding unbounded leads-to property.

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Section: Adding a Single Bounded-time Leads-to Propertymentioning

confidence: 99%

Revising UNITY Programs: Possibilities and Limitations

Ebnenasir

Kulkarni

Bonakdarpour

2006

Lecture Notes in Computer Science

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“…Standard algorithms for finding shortest paths [12,13] can be applied; the probabilities can be transformed into distances required by the standard methods by taking the negative logarithm of the goodness:…”

Section: G(g W)mentioning

confidence: 99%

Link Discovery in Graphs Derived from Biological Databases

Sevon

Eronen

Hintsanen

et al. 2006

Lecture Notes in Computer Science

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Abstract. Public biological databases contain vast amounts of rich data that can also be used to create and evaluate new biological hypothesis. We propose a method for link discovery in biological databases, i.e., for prediction and evaluation of implicit or previously unknown connections between biological entities and concepts. In our framework, information extracted from available databases is represented as a graph, where vertices correspond to entities and concepts, and edges represent known, annotated relationships between vertices. A link, an (implicit and possibly unknown) relation between two entities is manifested as a path or a subgraph connecting the corresponding vertices. We propose measures for link goodness that are based on three factors: edge reliability, relevance, and rarity. We handle these factors with a proper probabilistic interpretation. We give practical methods for finding and evaluating links in large graphs and report experimental results with Alzheimer genes and protein interactions.

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“…The arrows indicate the order of arrival of these sub-paths at node i. Once the Þrst two sub-paths have arrived at node i, we have our Þrst complete path with weight vector w(P ) = (7,4). If the constraints are L = (10,10) then the length of this path equals 0.7.…”

Section: Multi-constrained Bi-directional Searchmentioning

confidence: 99%

“…It may therefore be necessary to store in the computation more (sub-)paths then just the shortest. SAMCRA and TAMCRA use the k-shortest path approach [7], where in TAMCRA k is predeÞned by the user and in SAM-CRA k is adapted in the course of the computation to assure that the exact shortest path is found. 3.…”

Section: Hamcramentioning

confidence: 99%

Bi-directional Search in QoS Routing

Kuipers

Mieghem

2003

Quality for All

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Abstract. The "bi-directional search method" used for unicast routing is brießy reviewed. The extension of this method unicast QoS routing is discussed and an exact hybrid QoS algorithm HAMCRA that is partly based on bi-directional search is proposed. HAMCRA uses the speed of a heuristic when the constraints are loose and efficiently maintains exactness where heuristics fail. The performance of HAMCRA is simulated.

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Finding the k shortest paths

Cited by 446 publications

References 52 publications

Revising UNITY Programs: Possibilities and Limitations

Revising UNITY Programs: Possibilities and Limitations

Link Discovery in Graphs Derived from Biological Databases

Bi-directional Search in QoS Routing

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