{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:12:07Z","timestamp":1750306327219,"version":"3.41.0"},"reference-count":38,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2016,5,2]],"date-time":"2016-05-02T00:00:00Z","timestamp":1462147200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Institute for Mathematics and Its Applications"},{"DOI":"10.13039\/100000185","name":"U.S. Defense Advanced Research Projects Agency","doi-asserted-by":"crossref","award":["HR0011-07-1-0002"],"award-info":[{"award-number":["HR0011-07-1-0002"]}],"id":[{"id":"10.13039\/100000185","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000181","name":"U.S. Air Force Office of Scientific Research","doi-asserted-by":"crossref","award":["FA9550-09-1-0561, FA9550-12-1-0225, and FA9550-12-1-0418"],"award-info":[{"award-number":["FA9550-09-1-0561, FA9550-12-1-0225, and FA9550-12-1-0418"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Sen. Netw."],"published-print":{"date-parts":[[2016,5,12]]},"abstract":"<jats:p>\n            We consider the problem of fusing measurements in a sensor network, where the sensing regions overlap and data are nonnegative real numbers, possibly resulting from a count of indistinguishable discrete entities. Because of overlaps, it is generally impossible to fuse this information to arrive at an accurate value of the overall amount or count of material present in the union of the sensing regions. Here we study the computation of the range of overall values consistent with the data and provide several results. Posed as a linear programming problem, this leads to questions associated with the geometry of the sensor regions, specifically the arrangement of their nonempty intersections. We define a computational tool called the\n            <jats:italic>fusion polytope<\/jats:italic>\n            , based on the geometry of the sensing regions. Its properties are explored, and in particular, a topological necessary and sufficient condition for this to be in the positive orthant, a property that considerably simplifies calculations, is provided. We show that in two dimensions, inflated tiling schemes based on rectangular regions fail to satisfy this condition, whereas inflated tiling schemes based on hexagons do.\n          <\/jats:p>","DOI":"10.1145\/2903722","type":"journal-article","created":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T13:08:37Z","timestamp":1462280917000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Bounds on Multiple Sensor Fusion"],"prefix":"10.1145","volume":"12","author":[{"given":"Bill","family":"Moran","sequence":"first","affiliation":[{"name":"RMIT University, Melbourne, VIC, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fred","family":"Cohen","sequence":"additional","affiliation":[{"name":"University of Rochester, Rochester, NY, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zengfu","family":"Wang","sequence":"additional","affiliation":[{"name":"Northwestern Polytechnical University, Shaanxi, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sofia","family":"Suvorova","sequence":"additional","affiliation":[{"name":"RMIT University, Melbourne, VIC, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Douglas","family":"Cochran","sequence":"additional","affiliation":[{"name":"Arizona State University, AZ, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tom","family":"Taylor","sequence":"additional","affiliation":[{"name":"Arizona State University, AZ, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Farrell","sequence":"additional","affiliation":[{"name":"University of Melbourne, VIC, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen","family":"Howard","sequence":"additional","affiliation":[{"name":"Defence Science and Technology Group, Canberra BC, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,5,2]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/ACSSC.2006.356635"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","unstructured":"Paul Alexandroff and Heinz Hopf. 1935. Topologie. Springer Berlin Germany.  Paul Alexandroff and Heinz Hopf. 1935. Topologie. Springer Berlin Germany.","DOI":"10.1007\/978-3-662-02021-0"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-69170-9_3"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/AVSS.2010.29"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1951-0046635-9"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-30538-5_16"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(75)90041-6"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1021\/ja00291a006"},{"volume-title":"Linear Programming and Extensions","author":"Dantzig George B.","key":"e_1_2_1_9_1","unstructured":"George B. Dantzig . 1998. Linear Programming and Extensions . Princeton University Press , Princeton, NJ . George B. Dantzig. 1998. Linear Programming and Extensions. Princeton University Press, Princeton, NJ."},{"key":"e_1_2_1_10_1","volume-title":"Counting Targets: Building and Managing Aggregates in Wireless Sensor Networks. Technical Report P2002-10298","author":"Fang Qing","year":"2002","unstructured":"Qing Fang , Feng Zhao , and Leonidas Guibas . 2002 . Counting Targets: Building and Managing Aggregates in Wireless Sensor Networks. Technical Report P2002-10298 . Palo Alto Research Center (PARC) , Palo Alto, CA . Qing Fang, Feng Zhao, and Leonidas Guibas. 2002. Counting Targets: Building and Managing Aggregates in Wireless Sensor Networks. Technical Report P2002-10298. Palo Alto Research Center (PARC), Palo Alto, CA."},{"key":"e_1_2_1_11_1","series-title":"Lecture Notes in Computer Science","volume-title":"Algorithmic Aspects of Wireless Sensor Networks","author":"Gandhi Sorabh","unstructured":"Sorabh Gandhi , Rajesh Kumar , and Subhash Suri . 2008. Target counting under minimal sensing: Complexity and approximations . In Algorithmic Aspects of Wireless Sensor Networks . Lecture Notes in Computer Science , Vol. 5389 . Springer , 30--42. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-540-92862-1_4 10.1007\/978-3-540-92862-1_4 Sorabh Gandhi, Rajesh Kumar, and Subhash Suri. 2008. Target counting under minimal sensing: Complexity and approximations. In Algorithmic Aspects of Wireless Sensor Networks. Lecture Notes in Computer Science, Vol. 5389. Springer, 30--42. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-540-92862-1_4"},{"key":"e_1_2_1_12_1","volume-title":"Linear Programming: Methods and Applications","author":"Gass Saul I.","year":"2010","unstructured":"Saul I. Gass . 2010 . Linear Programming: Methods and Applications ( 5 th ed.). Dover Publications , New York, NY . Saul I. Gass. 2010. Linear Programming: Methods and Applications (5th ed.). Dover Publications, New York, NY.","edition":"5"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2008.IV.031"},{"volume-title":"Handbook of Combinatorics, R.&nbsp","author":"Gr\u00f6tschel Martin","key":"e_1_2_1_14_1","unstructured":"Martin Gr\u00f6tschel and L\u00e1szl\u00f3 Lov\u00e1sz . 1995. Combinatorial optimization . In Handbook of Combinatorics, R.&nbsp ;L. Graham, M. Gr\u00f6tschel, and L. Lov\u00e1sz (Eds.). Elsevier , North- Holland, Netherlands , 1541--1598. Martin Gr\u00f6tschel and L\u00e1szl\u00f3 Lov\u00e1sz. 1995. Combinatorial optimization. In Handbook of Combinatorics, R.&nbsp;L. Graham, M. Gr\u00f6tschel, and L. Lov\u00e1sz (Eds.). Elsevier, North-Holland, Netherlands, 1541--1598."},{"volume-title":"Algorithms and Combinatorics","author":"Gr\u00f6tschel Martin","key":"e_1_2_1_15_1","unstructured":"Martin Gr\u00f6tschel , L\u00e1szlo Lov\u00e1sz , and Alexander Schrijver . 1993. Geometric algorithms and combinatorial optimization . In Algorithms and Combinatorics . Springer-Verlag , Berlin, Germany . Martin Gr\u00f6tschel, L\u00e1szlo Lov\u00e1sz, and Alexander Schrijver. 1993. Geometric algorithms and combinatorial optimization. In Algorithms and Combinatorics. Springer-Verlag, Berlin, Germany."},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the 5th IEEE International Conference on Mobile Ad-Hoc and Sensor Systems (MASS\u201908)","author":"Guo Shuo","year":"2008","unstructured":"Shuo Guo , Tian He , Mohamed F. Mokbel , John A. Stankovic , and Tarek F. Abdelzaher . 2008. On accurate and efficient statistical counting in sensor-based surveillance systems . In Proceedings of the 5th IEEE International Conference on Mobile Ad-Hoc and Sensor Systems (MASS\u201908) . IEEE, Los Alamitos, CA, 24--35. DOI:http:\/\/dx.doi.org\/10.1109\/MAHSS. 2008 .4660038 10.1109\/MAHSS.2008.4660038 Shuo Guo, Tian He, Mohamed F. Mokbel, John A. Stankovic, and Tarek F. Abdelzaher. 2008. On accurate and efficient statistical counting in sensor-based surveillance systems. In Proceedings of the 5th IEEE International Conference on Mobile Ad-Hoc and Sensor Systems (MASS\u201908). IEEE, Los Alamitos, CA, 24--35. DOI:http:\/\/dx.doi.org\/10.1109\/MAHSS.2008.4660038"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.pmcj.2009.07.013"},{"key":"e_1_2_1_18_1","first-page":"175","article-title":"\u00dcber mengen konvexer k\u00f6rper mit gemeinschaftlichen punkten","volume":"32","author":"Helly Eduard","year":"1923","unstructured":"Eduard Helly . 1923 . \u00dcber mengen konvexer k\u00f6rper mit gemeinschaftlichen punkten . Jahresbericht der Deutschen Mathematiker-Vereinigung 32 , 175 -- 176 . Eduard Helly. 1923. \u00dcber mengen konvexer k\u00f6rper mit gemeinschaftlichen punkten. Jahresbericht der Deutschen Mathematiker-Vereinigung 32, 175--176.","journal-title":"Jahresbericht der Deutschen Mathematiker-Vereinigung"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1254850.1254864"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1167935.1167937"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1236360.1236426"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1109\/AVSS.2012.54"},{"volume-title":"Computational Methods for Protein Structure Prediction and Modeling, Y. Xu","author":"Liang Jie","key":"e_1_2_1_24_1","unstructured":"Jie Liang . 2007. Computation of protein geometry and its applications: Packing and function prediction . In Computational Methods for Protein Structure Prediction and Modeling, Y. Xu , D. Xu, and J. Liang (Eds.). Springer , New York, NY , 181--206. DOI:http:\/\/dx.doi.org\/10.1007\/978-0-387-68372-0_6 10.1007\/978-0-387-68372-0_6 Jie Liang. 2007. Computation of protein geometry and its applications: Packing and function prediction. In Computational Methods for Protein Structure Prediction and Modeling, Y. Xu, D. Xu, and J. Liang (Eds.). Springer, New York, NY, 181--206. DOI:http:\/\/dx.doi.org\/10.1007\/978-0-387-68372-0_6"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09680-3_14"},{"volume-title":"Modeling, Simulation, and Visual Analysis of Crowds","author":"Loy Chen Change","key":"e_1_2_1_26_1","unstructured":"Chen Change Loy , Ke Chen , Shaogang Gong , and Tao Xiang . 2013. Crowd counting and profiling: Methodology and evaluation . In Modeling, Simulation, and Visual Analysis of Crowds . Springer , 347--382. DOI:http:\/\/dx.doi.org\/10.1007\/978-1-4614-8483-7_14 10.1007\/978-1-4614-8483-7_14 Chen Change Loy, Ke Chen, Shaogang Gong, and Tao Xiang. 2013. Crowd counting and profiling: Methodology and evaluation. In Modeling, Simulation, and Visual Analysis of Crowds. Springer, 347--382. DOI:http:\/\/dx.doi.org\/10.1007\/978-1-4614-8483-7_14"},{"volume-title":"Understanding and Using Linear Programming","author":"Matousek Jiri","key":"e_1_2_1_27_1","unstructured":"Jiri Matousek and Bernd G\u00e4rtner . 2007. Understanding and Using Linear Programming . Springer-Verlag, Heidelberg , Germany . Jiri Matousek and Bernd G\u00e4rtner. 2007. Understanding and Using Linear Programming. Springer-Verlag, Heidelberg, Germany."},{"volume-title":"Proceedings of the 8th European Conference on Computer Vision (ECCV\u201904)","author":"Mittal Anurag","key":"e_1_2_1_28_1","unstructured":"Anurag Mittal and Larry S. Davis . 2004. Visibility analysis and sensor planning in dynamic environments . In Proceedings of the 8th European Conference on Computer Vision (ECCV\u201904) . 175--189. Anurag Mittal and Larry S. Davis. 2004. Visibility analysis and sensor planning in dynamic environments. In Proceedings of the 8th European Conference on Computer Vision (ECCV\u201904). 175--189."},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.5555\/1817271.1817297"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1109\/21.120060"},{"key":"e_1_2_1_31_1","volume-title":"Linhares-Sales","author":"Reed Bruce A.","year":"2003","unstructured":"Bruce A. Reed and Claudia L . Linhares-Sales . 2003 . Recent Advances in Algorithms and Combinatorics. Springer , New York, NY. Bruce A. Reed and Claudia L. Linhares-Sales. 2003. Recent Advances in Algorithms and Combinatorics. Springer, New York, NY."},{"volume-title":"Handbook of Combinatorics","author":"Schrijver Alexander","key":"e_1_2_1_32_1","unstructured":"Alexander Schrijver . 1995. Polyhedral combinatorics . In Handbook of Combinatorics , R. L. Graham, M. Gr\u00f6tschel, and L. Lov\u00e1sz (Eds.). Elsevier , Berlin, Germany , 1649--1704. Alexander Schrijver. 1995. Polyhedral combinatorics. In Handbook of Combinatorics, R. L. Graham, M. Gr\u00f6tschel, and L. Lov\u00e1sz (Eds.). Elsevier, Berlin, Germany, 1649--1704."},{"volume-title":"Buildings of Spherical Type and Finite BN-Pairs","author":"Tits Jacques","key":"e_1_2_1_33_1","unstructured":"Jacques Tits . 1974. Buildings of Spherical Type and Finite BN-Pairs . Vol. 386 . Springer-Verlag , Berlin, Germany . Jacques Tits. 1974. Buildings of Spherical Type and Finite BN-Pairs. Vol. 386. Springer-Verlag, Berlin, Germany."},{"key":"e_1_2_1_34_1","volume-title":"Graph Theoretical Problems and Related Polytopes: Stable Sets and Perfect Graphs. Retrieved","author":"Wagler Annegret K.","year":"2016","unstructured":"Annegret K. Wagler . 2003. Graph Theoretical Problems and Related Polytopes: Stable Sets and Perfect Graphs. Retrieved April 1, 2016 , from http:\/\/www.oil.di.univaq.it\/ricerca\/eventi\/seminarioWagler\/BlockSeminar.pdf. Annegret K. Wagler. 2003. Graph Theoretical Problems and Related Polytopes: Stable Sets and Perfect Graphs. Retrieved April 1, 2016, from http:\/\/www.oil.di.univaq.it\/ricerca\/eventi\/seminarioWagler\/BlockSeminar.pdf."},{"key":"e_1_2_1_35_1","volume-title":"Proceedings of IEEE INFOCOM (INFOCOM\u201912)","author":"Wu Dengyuan","year":"2012","unstructured":"Dengyuan Wu , Dechang Chen , Kai Xing , and Xiuzhen Cheng . 2012 . A statistical approach for target counting in sensor-based surveillance systems . In Proceedings of IEEE INFOCOM (INFOCOM\u201912) . IEEE, Los Alamitos, CA, 226--234. DOI:http:\/\/dx.doi.org\/10.1109\/INFCOM. 2012.6195613 10.1109\/INFCOM.2012.6195613 Dengyuan Wu, Dechang Chen, Kai Xing, and Xiuzhen Cheng. 2012. A statistical approach for target counting in sensor-based surveillance systems. In Proceedings of IEEE INFOCOM (INFOCOM\u201912). IEEE, Los Alamitos, CA, 226--234. DOI:http:\/\/dx.doi.org\/10.1109\/INFCOM.2012.6195613"},{"volume-title":"The Art of Wireless Sensor Networks","author":"Wu Dengyuan","key":"e_1_2_1_36_1","unstructured":"Dengyuan Wu , Bowu Zhang , Hongjuan Li , and Xiuzhen Cheng . 2014. Target counting in wireless sensor networks . In The Art of Wireless Sensor Networks . Springer , Berlin, Germany , 235--269. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642-40066-7_7 10.1007\/978-3-642-40066-7_7 Dengyuan Wu, Bowu Zhang, Hongjuan Li, and Xiuzhen Cheng. 2014. Target counting in wireless sensor networks. In The Art of Wireless Sensor Networks. Springer, Berlin, Germany, 235--269. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642-40066-7_7"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comcom.2007.05.012"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1109\/INFCOM.2011.5935041"},{"volume-title":"Proceedings of the 2nd Mexican Conference on Pattern Recognition (MCPR\u201910)","author":"Zou Chengming","key":"e_1_2_1_39_1","unstructured":"Chengming Zou and Edwin R. Hancock . 2010. Face recognition using simplicial complexes . In Proceedings of the 2nd Mexican Conference on Pattern Recognition (MCPR\u201910) . 22--29. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642-15992-3_3 10.1007\/978-3-642-15992-3_3 Chengming Zou and Edwin R. Hancock. 2010. Face recognition using simplicial complexes. In Proceedings of the 2nd Mexican Conference on Pattern Recognition (MCPR\u201910). 22--29. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642-15992-3_3"}],"container-title":["ACM Transactions on Sensor Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2903722","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2903722","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:54:33Z","timestamp":1750222473000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2903722"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,2]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,5,12]]}},"alternative-id":["10.1145\/2903722"],"URL":"https:\/\/doi.org\/10.1145\/2903722","relation":{},"ISSN":["1550-4859","1550-4867"],"issn-type":[{"type":"print","value":"1550-4859"},{"type":"electronic","value":"1550-4867"}],"subject":[],"published":{"date-parts":[[2016,5,2]]},"assertion":[{"value":"2014-10-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-03-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-05-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}