Combining Speedup Technique

Combining speedup techniques based on landmarks and containersFiras M Abu Hassan 20911833

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Outline Introduction

Main Techniques Related Work Landmarks techniques Geometric Containers Combining both landmarks and geometrics containers Experimental analysis Conclusion

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Introduction Compute the shortest path between source and

destination in the graph using DIJKSTRA algorithm. Running time = O(V2), O(E logV) many of real world application such as mobile routing, route planning in road networks, railway network. Very slow when it used with huge dataset. there are many techniques used to improve and speed up the original DIJKSTRA algorithm

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Main Techniques In this paper the Authors focus into two

techniques in order to speed up the traditional DIJKSTRA algorithm:Landmarks Techniques 2. Geometric Containers1.

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Related Workthere are many other techniques which solve special case of DIJKSTRA with better running time, as the follows: 1. Goal directed search: Modification of edge weights with help of potential function: Goal: directing search towards target

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Related Work (cont) modify the priority of a node v by dist(v)+pt(v) the length of an s-t path with modified edge

lengths is the same up to the constant pt(s)+pt(t). this techniques will speed up the original algorithm with factor of 1.5.

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Related Work (cont)2. Bidirectional search:

executes DIJKSTRA algorithm simultaneously forwards from the source s and backwards from the target t . Once some node has been visited from both directions, then the shortest path can be derived by sum the both distances. This techniques will speed up the original algorithm with factor of 2.

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Example 1 Example 2

Related Work (cont)3. Multilevel approach : divided the original graph into multi sub small graph and implements the original DIJKSTRA algorithm into these sub graphs. this step will leads to decrease the search space for original algorithm and decrease the number of visited node. this techniques will speed up the original algorithm with factor of 3.5.

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Related Work (cont)4. Shortest-path containers: Speedup factors in the range between 10 and 20 can

be achieved.

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Related Work (cont) Goal-Directed Search and Bidirectional Search

Goal-Directed Search and Multilevel Approach Bidirectional Search and Shortest-Path

Containers . . . . etc10

Landmarks techniques which it used to reduce the search space for

DIJKSTRA algorithm updates the traditional DIJKSTRA algorithm to compute the distance from landmark to the target by using potential (u) heuristic value. Select any vertex randomly to be the first landmarks and then calculate the distance to all nearest vertex and locate it into queue.

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Landmarks techniques(cont) Then the vertex with minimum distance to the

landmarks will be the first vertex deleted from the queue and so on until reach to last vertex to be deleted from the queue to be selected as new landmarks and repeat the process until the required number of landmarks is selected. The search space and the number of node visited

will be decreased.12

Geometric Containers improve the traditional algorithm by reducing

the search space for DIJKSTRA algorithm by just contain nodes which are potentially useful for shortest path computations , not all nodes in the graph. For each edge e, determine all nodes Se that are reachable via e on a shortest path. For each edge e, store a geometric object around Se . (Bounding Box)13

Geometric Containers(cont) When an edge e is reached, the boundary values

of that edge e is checked to see if it contains the target node. If the target is present in the container then the edge is selected otherwise the edge is discarded. The number of visited nodes is reduced and also the search space.

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Combining both landmarks and geometrics containers improve the speedup by:

terminates the search procedure once the target is reached. 2. selecting just the effected node when selecting shortest path from vertex to target. -Not all nodes as in DIJKSTRA. 3. reduce the number of vertex visited.1.

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Experimental analysis landmarks in random graph

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Experimental analysis landmarks in planar graph

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Experimental analysis geometric containers in random graph

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Experimental analysis geometric containers in planar graph

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Combination of Landmarks and Geometric Containers applied to random Graphs

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Combination of Landmarks and Geometric Containers applied to planar Graphs

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Conclusion The main two techniques that used to improve

the DIJKSTRA algorithm such as landmarks and geometric containers both analyzed in various type of the graph such as random graph and planar graph and each speedup technique work well with specific kind of the graph, which can also be applied to various other graph types. The heuristic value obtained by using landmark reduce the number of vertex visited but the running time of the technique marginally high due to computation overhead during vertex distance updating when selecting new landmark.22

Conclusion The second technique (geometric containers)

achieved speedup depending on the number of vertex visited through evaluation the shortest path but were nearly equal in running time to the traditional algorithm. combining both speedup techniques based on landmarks and containers was able to perform better result under the same experimental setup compared to other technique that achieve time speedup by 1.12 in time domain and achieve speedup in number of vertex visited with 1.7.23

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