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Course: CS 056000, Fall 2009School: Dallas
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4 Graph Lecture Search Breadth First Search animation Initialize 2 1 1 pred(1) all Unmark= 0 nodes in N; next := 1 order(next) = Mark node s 1 LIST:= {1} LIST 1 next 1 3 5 6 4 8 7 9 Select a node i in LIST 2 1 1 In breadth first search, i is the first node in LIST 3 5 6 4 8 7 9 LIST 1 next 1 If node i is incident to an admissible arc... 2 2 1 1 Next := an j Mark Node Select Next + 1 admissible add j to LIST...
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4
Graph Lecture Search
Breadth First Search animation
Initialize
2 1 1 pred(1) all Unmark= 0 nodes in N; next := 1 order(next) = Mark node s 1 LIST:= {1} LIST 1 next 1 3 5 6 4 8 7 9
Select a node i in LIST
2 1 1 In breadth first search, i is the first node in LIST 3 5 6 4 8 7 9
LIST
1 next 1
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4
8 7
5 3 6
pred(j) := i order(j) := next arc (i,j)
9
LIST
1
2 next 2 1
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4
8 7
5 3
3 6
pred(j) := i order(j) := next arc (i,j)
9
LIST
1
2
5 next 3 2
If node i is incident to an admissible arc...
2 2 1 1
Next := an Mark Node Select Next + 1
4
8 7
5 3
3 6
j 9 4
admissible pred(j) := next := i order(j) arc (i,j)
add j to LIST
LIST
1
2
5
3 next 4 3 2
If node i is not incident to an admissible arc...
2 2 1 1 3 5 4 8 7 6 9
3
Delete node i from LIST
4
LIST
1
2
5
3 next 4 3 2
Select Node i
2 2 1 1 3 5 4 8 7 6 9
3
The first node on LIST becomes node i LIST 1 2 5
4
3 next 4 3 2
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4
5
8 7
5 3
3 6
pred(j) := i order(j) := next arc (i,j)
9
4
LIST
1
2
5
3
4 next 5 4 3 2
If node i is not incident to an admissible arc...
2 2 1 1 Delete node i from LIST 3 5 4 5 8 7 6 9
3
4
LIST
1
2
5
3
4 next 5 4 3 2
Select a node
2 2 1 1 The first node on LIST becomes node i 3 5 4 5 8 7 6 9
3
4
LIST
1
2
5
3
4 next 5 4 3 2
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4
5
8 7
5 3
3 6 6
pred(j) := i order(j) := next arc (i,j)
9
4
LIST
1
2
5
3
4
6 6 5 4 3 2
next
If node i is not incident to an admissible arc...
2 2 1 1 Delete node i from LIST 3 5 4 5 8 7 6 6 9
3
4
LIST
1
2
5
3
4
6 6 5 4 3 2
next
Select node 3
2 2 1 1 node 3node 3 delete is not incident to from LIST any admissible arcs LIST 1 2 5 3 5 4 5 8 7 6 6 9
3
4
3
4
6 6 5 4 3 2
next
Select a node
2 2 1 1 i:=4 3 4 6 6 5 4 5 8 7 9
3
LIST
1
2
5
3
4
6 6 5 4 3 2
next
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4
5
87 7
5 3
3 6 6
pred(j) := i order(j) := next arc (i,j)
9
4
LIST
1
2
5
3
4
6
8 7 6 5 4 3 2
next
If node i is not incident to an admissible arc...
2 2 1 1 Delete node i from LIST 3 5 4 5 87 7 6 6 9
3
4
LIST
1
2
5
3
4
6
8 7 6 5 4 3 2
next
Select node i
2 2 1 1 i := 6 3 4 6 6 9 5 4 5 87 7
3
LIST
1
2
5
3
4
6
8 7 6 5 4 3 2
next
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4
5
87 7 8
5 3
3 6 6
pred(j) := i order(j) := next arc (i,j)
9
4
LIST
1
2
5
3
4
6
8 8 7 6 5 4 3 2
7
next
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4
5
87 7 8
5 3
3 6 6
pred(j) := i order(j) := next arc (i,j)
9 9
4
LIST
1
2
5
3
4
6
8 9 8 7 6 5 4 3 2
7
9
next
If node i is not incident to an admissible arc...
2 2 1 1 Delete node i from LIST 3 5 4 5 87 7 8 6 6 9 9
3
4
LIST
1
2
5
3
4
6
8 9 8 7 6 5 4 3 2
7
9
next
Select node 8
2 2 1 1 node 8 is not incident to an admissible arc; delete it from LIST LIST 1 2 5 3 5 4 5 87 7 8 6 6 9 9
3
4
3
4
6
8 9 8 7 6 5 4 3 2
7
9
next
Select node 7
2 2 1 1 node 7 is not incident to an admissible arc; delete it from LIST LIST 1 2 5 3 5 4 5 87 7 8 6 6 9 9
3
4
3
4
6
8 9 8 7 6 5 4 3 2
7
9
next
Select node 9
2 2 1 1 node 9 is not incident to an admissible arc; delete it from LIST LIST 1 2 5 3 5 4 5 87 7 8 6 6 9 9
3
4
3
4
6
8 9 8 7 6 5 4 3 2
7
9
next
5
Summary Find the shortest path from s to each other node path length = number of arcs on path; Determine the connected components of a network; Determine breadth first search.
Next
Determine depth first search; Shows up in other algorithms as well. Determine topological sort; Running time is O(n+m) using simple data structures and algorithms. Very important for preprocessing.
Depth First Search animation
Initialize
2 1 1 pred(1) all Unmark= 0 nodes in N; next := 1 order(next) = Mark node s 1 LIST:= {1} LIST 1 next 1 3 5 6 4 8 7 9
Select a node i in LIST
2 1 1 In depth first search, i is the last node in LIST 3 5 6 4 8 7 9
LIST
1 next 1
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4
8 7
5 3 6
pred(j) := i order(j) := next arc (i,j)
9
LIST
1
2 next 2 1
Select the last node on LIST
2 2 1 1 3 5 6 4 8 7 9
Node 2 gets selected
LIST
1
2 next 2 1
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4 3 5 7 6
8
pred(j) := i order(j) := next arc (i,j)
3
9
LIST
1
2
4 next 3 2 1
Select
2 2 1 1 Select the last node on LIST 3 5 6 4 3 7 9 8
LIST
1
2
4 next 3 2 1
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4 3 5 7 6
8 4
pred(j) := i order(j) := next arc (i,j)
3
9
LIST
1
2
4
8 next 4 3 2 1
Select
2 2 1 1 Select the last node on LIST 3 5 6 4 3 7 9 8 4
LIST
1
2
4
8 next 4 3 2 1
If node i is not incident to an admissible arc...
2 2 Delete node i from LIST 1 1 3 5
4 3 7 6
8 4
9
LIST
1
2
4
8 next 4 3 2 1
Select
2 2 1 1 Select the last on node LIST 3 5 6 4 3 7 9 8 4
LIST
1
2
4
8 next 4 3 2 1
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4 3 5 5 7 6
8 4
pred(j) := i order(j) := next arc (i,j)
3
9
LIST
1
2
4
5 8 next 5 4 3 2 1
Select
2 2 1 1 Select the last node on LIST 3 5 5 4 3 7 6 9 8 4
LIST
1
2
4
5 8 next 5 4 3 2 1
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4 3 5 5 7 6 6
8 4
pred(j) := i order(j) := next arc (i,j)
3
9
LIST
1
2
4
5 8
6 next 6 5 4 3 2 1
Select the last node on LIST
2 2 1 1 Select node 6 3 6 6 9 5 5 4 3 7 8 4
LIST
1
2
4
5 8
6 next 6 5 4 3 2 1
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4 3 5 5 7 6 6
8 4
pred(j) := i order(j) := next arc (i,j)
3
9 7
LIST
1
2
4
5 8
6
9 7 6 5 4 3 2 1
next
Select the last node on LIST
2 2 1 1 Select node 9 3 6 6 9 7 5 5 4 3 7 8 4
LIST
1
2
4
5 8
6
9 7 6 5 4 3 2 1
next
If node i is incident to an admissible arc...
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4 3 5 5 7 8 6 6
8 4
pred(j) := i order(j) := next arc (i,j)
3
9 7
LIST
1
2
4
5 8
6
9
7 8 7 6 5 4 3 2 1
next
Select the last node on LIST
2 2 1 1 Select node 7 3 6 6 9 7 5 5 4 3 7 8 8 4
LIST
1
2
4
5 8
6
9
7 8 7 6 5 4 3 2 1
next
If node i is not incident to an admissible arc...
2 2 1 1 Delete node 7 from LIST 3 5 5 4 3 7 8 6 6 9 7 8 4
LIST
1
2
4
5 8
6
9
7 8 7 6 5 4 3 2 1
next
Select node 9
2 2 1 1 Delete node 9 But node 9 is from LIST not incident to an admissible arc. LIST 1 2 4 3 5 5 4 3 7 8 6 6 9 7 8 4
5 8
6
9
7 8 7 6 5 4 3 2 1
next
Select node 6
2 2 1 1 Delete node 6 But node 6 is from LIST not incident to an admissible arc. LIST 1 2 4 3 5 5 4 3 7 8 6 6 9 7 8 4
5 8
6
9
7 8 7 6 5 4 3 2 1
next
Select node 5
2 2 1 1 But node 5 is Delete node 5 not incident from LIST to an admissible arc. LIST 1 2 4 3 5 5 4 3 7 8 6 6 9 7 8 4
5 8
6
9
7 8 7 6 5 4 3 2 1
next
Select node 4
2 2 1 1 Delete node 4 But node 4 is from LIST not incident to an admissible arc. LIST 1 2 4 3 5 5 4 3 7 8 6 6 9 7 8 4
5 8
6
9
7 8 7 6 5 4 3 2 1
next
Select node 2
2 2 1 1 Delete node 2 But node 2 is from LIST not incident to an admissible arc. LIST 1 2 4 3 5 5 4 3 7 8 6 6 9 7 8 4
5 8
6
9
7 8 7 6 5 4 3 2 1
next
Select node 1
2 2 1 1
Next := an j Mark Node Select Next + 1 admissible add j to LIST
4 3 5 5 7 8 6 6
8 4
pred(j) := i order(j) := next arc (i,j)
3 9
9 7
LIST
1
3 2
4
5 8
6
9
7 9 8 7 6 5 4 3 2 1
next
Select node 3
2 2 1 1 Delete node 3 But node 3 is from LIST not incident to an admissible arc. LIST 1 3 2 4 3 9 5 5 4 3 7 8 6 6 9 7 8 4
5 8
6
9
7 9 8 7 6 5 4 3 2 1
next
Select node 1
2 2 1 1 Delete node 1 But node 1 is from LIST not incident to an admissible arc. LIST 1 3 2 4 3 9 5 5 4 3 7 8 6 6 9 7 8 4
5 8
6
9
7 9 8 7 6 5 4 3 2 1
next
LIST is empty
2 2 1 1 The algorithm ends! 3 9 5 5 4 3 7 8 6 6 9 7 8 4
LIST
1
3 2
4
5 8
6
9
7 9 8 7 6 5 4 3 2 1
next
The depth first search tree
Note that each induced subtree has consecutively labeled nodes 1 1 22 4 3 4 8 5 5 6 6 9 7 7 8 3 9
Topological Ordering animation
Initialization
6 "Next" the LIST is will Determine b...
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Downloaded 09 Mar 2007 to 129.101.74.157. Redistribution subject to AIP license or copyright, see http:/jap.aip.org/jap/copyright.jspDownloaded 09 Mar 2007 to 129.101.74.157. Redistribution subject to AIP license or copyright, see http:/jap.aip.org/jap/c
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Western Michigan - CS - 6030
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East Los Angeles College - MEETING - 020116
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East Los Angeles College - MEETING - 020116
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UPenn - ESE - 534
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UPenn - ESE - 534
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George Mason - DOCUMENT - 22415
LAND USE AND PHYSICAL FACILITIES COMMITTEE BOARD OF VISITORSWednesday, December 6, 2006AGENDAI. Call to Order II. Approval of Minutes a. Meeting of October 4, 2006 (ACTION ITEM).F-2 b. Meeting of October 25, 2006 (ACTION ITEM).F-6 Old Business New Busi
Carnegie Mellon - THEO - 20
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Carnegie Mellon - THEO - 20
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FGCU - CGS - 1100
Weekly SalesPage 1Total Weekly Sales$900,000 $800,000$700,000$600,000 $500,000 $400,000 $300,000$200,000$100,000 $0BostonMiamiChicagoSan Diego
ASU - MAT - 119
MAT 119 Evaluate the following. Assume that x is an integer greater than 2. 1) 13P5 2) 13P8 3) 15C4 4) 15C11 5) xPx 2Practice 26)xCx 37) In the National Football League, there are 16 teams in the NFC and 16 teams in the AFC. In the Superbowl, one tea
Lake County - AE - 498
Stanley: The Robot That Won the DARPA Grand ChallengeA Look Into Laser Terrain MappingMeet Stanley VWTouareg R5 Roof rack5 laser sensorsRanges to 25m in front of vehicleStanley Software SystemVehicle State EstimationTwo different state estimation
Cornell - NELS - 39
Monoclausal Question Word Coordinations Across Languages Andreas Haida & Sophie Repp (Humboldt University Berlin) It has been claimed (e.g. [v]) that in questions with conjoined question words, or Q(uestion) W(ord) C(oordination)s, only multiple wh-fronti