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S1 Computer Science

创建日期：2024-04-09 17:21:21

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Computer Science

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Computer Science 720 S1

Assignment 2 (Bounded Treewidth Algorithms)
Due: Friday, April 23, 11:59pm
Requirements
In this assignment you will learn how to use and understand the t-parse data structure for graphs
of bounded pathwidth/treewidth. We will do some basic programming regarding the t-parse repre-
sentation of graphs.
We use the following t-parse input format for graphs of bounded treewidth. The first token will be
a positive integer t ≤ 9 denoting the pathwidth/treewidth of the graph (i.e., it indicates a t-parse
will follow). The interpretation for the remaining tokens are given in the next table.
token semantic meaning
i a vertex operator i, represented as an integer, where 0 ≤ i ≤ t ≤ 9
ij an edge operator (i, j) where t ≥ i > j ≥ 0 (note: no space between i and j)
( a begin marker for a pathwidth t-parse (can be nested for treewidth t-parses)
) an end marker for a pathwidth/treewidth t-parse
Thus, if you read/encounter the two tokens ‘)’ and ‘(’ in sequence then this denotes a circle plus
⊕ operator. Note that it is guaranteed that each right token ‘(’ will have a matched left token ‘)’.
Each ’(’ except first token must be preceded by a parenthesis and ’)’ may be succeeded “up the parse
tree” by pathwidth operators. We assume boundary vertices 0, 1, . . . , t precede the first token of a
pathwidth t-parse (and these empty boundaried graph axioms are not given in the input format).
Assume left-associativity for all operators and at least one space between each of them, including
the parentheses.
For each part of the assignment the input will consist of several test cases, each on its own line. The
input is terminated by a t = 0 case, which is also processed.
1
Problem 1: Parse and Extract Graph
You need to output an adjacency list representation using a sorted ‘CompSci 220 graph format’.
Here the first line is an integer n representing the order of the graph. The next n lines consist of a
(sorted integer) adjacency lists, for vertices indexed 0 to n− 1, of neighbor indices. To have unique
graph, the vertex indices are assigned labels to vertices in the same order as the new vertex operators
appear in the t-parse from left-to-right.
The following show typical input instances and expected output. Note that you can assume that
each input graph fits on one line.
Sample input
2 ( 10 21 1 10 21 0 10 20 2 20 21 )
2 ( ( 10 21 1 10 21 1 21 10 ) ( 21 2 21 20 ) ( 10 ) )
4 ( ( 10 20 30 41 4 41 31 ) ( ( 40 21 32 42 ) ( 10 0 43 10 20 ) ) )
0 ( ( 0 ) ( 0 0 ) )
Sample output
6
1 3
0 2
1 3 4
0 2 4 5
2 3 5
3 4
6
1 2 3 4
0 2
0 1 3 4
0 2
0 2 5
4
7
1 2 3 5
0 2 3 4 5 6
0 1 3 5
0 1 2 5
1
0 1 2 3
1
4
2
Problem 2: Weighted Independent Sets
In this part of the assignment you will learn how to exploit the structure of bounded pathwidth/treewidth
for a known hard graph problem:
Problem: Degree-Weighted Independent Set (DWIS)
Input: (undirected) Graph G = (V,E)
Question: Let the weight of each vertex be its degree (number of vertex neighbors).
What is the largest sum of vertex weights over all independent sets of vertices?
That is, maxV ′⊆V
∑
v∈V ′ deg(v) where for all {v1, v2} ⊆ V ′ we have (v1, v2) 6∈ E.
Your main requirements are to do the following.
1. For input graph of bounded pathwidth (in t-parse representation described above), determine
the DWIS.
2. Extend your linear-time program for item 1 for input of bounded treewidth.
The following show typical input instances. Again you can assume each input t-parse graph fits on
one line.
Sample input output
2 ( 10 21 1 10 21 0 10 20 2 20 21 ) 7
2 ( ( 10 21 1 10 21 1 21 10 ) ( 21 2 21 20 ) ) 7
4 ( ( 10 20 30 41 4 41 31 ) ( ( 40 21 32 42 ) ( 10 0 43 10 20 ) ) ) 6
3 ( 32 31 30 20 21 10 0 10 20 21 1 10 21 1 10 21 1 10 0 10 30 20 ) 11
2 ( 21 2 21 2 21 20 1 10 1 10 1 21 1 10 2 21 1 10 21 2 21 1 10 2 20 0 20 10 ) 16
3 ( ( 30 32 21 10 1 10 21 2 21 32 1 21 10 31 1 21 10 31 ) ( 20 21 32 2 21 32 ) 0 21 10 30 20 ) 14
4 ( 10 20 30 40 43 21 32 2 20 21 42 0 30 40 10 2 21 3 30 31 4 41 43 42 40 ) 13
0 ( 0 0 ) 0
Submission and Marks
All input should be taken from the keyboard (stdin) and output to the console (stdout). There will
be two test cases for each of our problems.
The first data set will only contain pathwidth t-parses and are worth 3 marks. The slightly harder
treewidth t-parse input cases will be worth 2 marks each. This assignment is worth 10% of your
final grade, where both Problems 1 and 2 are worth 5 marks each. Partial marks may be awarded
later (after due date) if determined to be close to correct.

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FE 825 IERG 5130 STAT 8178 EE161 ADS2 G54FUZ CS326 113B ECN 226 QBUS6860 ELEC3202 COMP9334 MGT11B MET CS 777 STA238 00099F Python SMM306 CMT206 EC116 SP MAST90084 CS480/680 BCPM0091 CMPT 300 ECON2209 FY20 STAT 432 CVEN9625 MATH1712 CMP9771M CMP3750M CIS 325 AI506 MAT344H1S MGT7180 PSTAT 160B CSYS5010 1D STAT 453/558 ME152B STA304H1F CSCI-128 ME428 CO3002 FINE 7640 COMP3234 ECSE 223 EE497 – 3D MATH5905 ECS648U ENG5009 MATH10242 EC665 A CPI221 ISOM5220 MACE40402 MGT B456F COMP9315 AFM 113 STAT 778 CS 564 MA231 CS 230 CS 124 COMP5511 CSC317 ITEC1010 ELEC207 INFT 3019 7CCMFM06 EE 161 5G ECLT5810 MATH 7349 CS526 O2 COMP90054 ELE00063M ACCT5034 ARC1015 CSCI 40 CSCI E40 FIN 524B CS 462 389COM CMT309 MFIN703 COMP4250 STA304 STA304H1S STA 1003 FIN 448 BUFN 732 CS520 CVEN3701 ECMT6006 PHAS0100 CSIT314 MDIA 5028 CSCI 2134 MAT 451 CMPT 459 STAT 457 INFO20003 COMP4141 IELE8066 F540 ECM9 CSE 6321 FIN 430 MATH3911 BFC5916 COMP1011 EEE 6209 STATS 240 CW3 COMP206 COMP1003 4331W ISE 530 CMPT 295 MATH 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COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 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ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 ACCOUNTING BUSS1040 CHEM 181 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