{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T12:35:26Z","timestamp":1778070926673,"version":"3.51.4"},"publisher-location":"Berlin, Heidelberg","reference-count":32,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540651420","type":"print"},{"value":"9783540495437","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1998]]},"DOI":"10.1007\/3-540-49543-6_10","type":"book-chapter","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T02:58:05Z","timestamp":1181185085000},"page":"116-130","source":"Crossref","is-referenced-by-count":14,"title":["Robotic Exploration, Brownian Motion and Electrical Resistance"],"prefix":"10.1007","author":[{"given":"Israel A.","family":"Wagner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Lindenbaum","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alfred M.","family":"Bruckstein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[1999,6,11]]},"reference":[{"key":"10_CR1","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/0166-218X(94)90008-6","volume":"55","author":"E. M. Arkin","year":"1994","unstructured":"Arkin E. M., Hassin R., \u201cApproximation Algorithms for the Geometric Covering Salesman Problem,\u201d Discrete Applied Math. 55, pp 197\u2013218, 1994.","journal-title":"Discrete Applied Math."},{"key":"10_CR2","doi-asserted-by":"crossref","unstructured":"Aleliunas R., Karp R.M., Lipton R. J., Lovasz L., Rakoff C., \u201cRandom Walks, Universal Traversal Sequences, and the Complexity of Maze Problems,\u201d in 20\u2019th Annual Symposium on Foundations of Computer Science, p. 218\u2013223, San Juan, Puerto Rico, October 1979.","DOI":"10.1109\/SFCS.1979.34"},{"issue":"1","key":"10_CR3","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/BF01047002","volume":"4","author":"D. J. Aldous","year":"1991","unstructured":"Aldous D. J., \u201cThreshold Limits for Cover Times,\u201d Jornal of Theoretical Probability, Vol. 4, No. 1, 1991, pp. 197\u2013211.","journal-title":"Jornal of Theoretical Probability"},{"key":"10_CR4","volume-title":"Geomtery II","author":"M. Berger","year":"1987","unstructured":"Berger M., Geomtery II, Springer-Verlag, Berlin-Heidelberg 1987."},{"key":"10_CR5","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/BF00710793","volume":"2","author":"G. Giralt","year":"1995","unstructured":"Giralt G., Weisbin C., (Editors), Special issue on autonomous robots for planetary exploration, Autonomous Robots, 2 (1995) pp. 259\u2013362.","journal-title":"Autonomous Robots"},{"key":"10_CR6","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/BF00735341","volume":"1","author":"T. Balch","year":"1994","unstructured":"Balch T., Arkin R. C., \u201cCommunication in reactive multiagent robotic systems,\u201d Autonomous Robots, 1 (1994) pp. 27\u201352.","journal-title":"Autonomous Robots"},{"key":"10_CR7","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1006\/inco.1993.1054","volume":"106","author":"R. Baeza-Yates","year":"1993","unstructured":"Baeza-Yates R., Culberson J. C., Rawlins G. J. E., \u201cSearching in the Plane,\u201d Information and Computation, 106 (1993) pp. 234\u2013252.","journal-title":"Information and Computation"},{"issue":"2","key":"10_CR8","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1137\/0218018","volume":"18","author":"A. Bar-Noy","year":"1989","unstructured":"Bar-Noy A., Borodin A., Karchemer M., Linial N., Werman M., \u201cBounds on Universal Sequences,\u201d SIAM J. Comput., Vol. 18, No. 2, pp.268\u2013277, (1989).","journal-title":"SIAM J. Comput."},{"key":"10_CR9","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/0196-6774(87)90019-8","volume":"8","author":"M.F. Bridgland","year":"1987","unstructured":"Bridgland M.F., \u201cUniversal Traversal Sequences for Paths and Cycles,\u201d J. of Alg., 8, (1987), pp.395\u2013404.","journal-title":"J. of Alg."},{"issue":"2","key":"10_CR10","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1137\/S0097539790190144","volume":"23","author":"A. Z. Broder","year":"1994","unstructured":"Broder A. Z., Karlin A. R., Raghavan P., Upfal E., \u201cTrading Space for Time in Undirected s-t Connectivity,\u201d SIAM J. COMPUT., Vol. 23, No. 2, pp. 324\u2013334, April 1994.","journal-title":"SIAM J. COMPUT."},{"key":"10_CR11","doi-asserted-by":"crossref","unstructured":"Chandra A. K., Raghavan P., Ruzzo W. L., Smolensky R., Tiwari P., \u201cThe Electrical Resistance of a Graph Captures its Commute and Cover Times,\u201d Proc. 21st ACM STOC, (1989), pp. 574\u2013586.","DOI":"10.1145\/73007.73062"},{"key":"10_CR12","doi-asserted-by":"crossref","unstructured":"Chin W. P., Ntafos S., \u201cOptimum Watchman Routes,\u201d 2\u2019nd Annual Symposium on Computational Geometry, Yorktown Heights, NY, June 2\u20134, 1986, pp. 24\u201333.","DOI":"10.1145\/10515.10518"},{"key":"10_CR13","doi-asserted-by":"crossref","DOI":"10.5948\/UPO9781614440222","volume-title":"Random Walks and Electric Networks","author":"P. G. Doyle","year":"1984","unstructured":"Doyle P. G., Snell J. L., Random Walks and Electric Networks, Mathematical Association of America, Washington, D. C., 1984."},{"key":"10_CR14","doi-asserted-by":"crossref","unstructured":"Dudek G., Jenkin M., Milios E., Wilkes D., \u201cRobotic Exploration as Graph Construction,\u201d IEEE Trans. on Robotics and Automation, Vol. 7, No. 6, Dec. 1991.","DOI":"10.1109\/70.105395"},{"key":"10_CR15","doi-asserted-by":"crossref","unstructured":"Deng X., Mirzaian A., \u201cCompetitive Robot Mapping with Homogeneous Markers,\u201d IEEE Trans. on Robotics and Automation, Vol. 12, No.4, Aug. 1996.","DOI":"10.1109\/70.508436"},{"issue":"5","key":"10_CR16","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1177\/027836499201100501","volume":"11","author":"M. Erdmann","year":"1988","unstructured":"Erdmann M., \u201cRandomization in robot tasks,\u201d Int. J. Robot. Res., 11(5):399\u2013436, October 1992. Hall P., Introduction to the Theory of Coverage Processes, John Wiley & Sons, New York, 1988","journal-title":"Int. J. Robot. Res."},{"key":"10_CR17","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0921-8890(94)00034-Y","volume":"14","author":"C. Hofner","year":"1995","unstructured":"Hofner C., Schmidt G., \u201cPath planning and guidance techniques for an autonomous mobile cleaning robot,\u201d Robotics and Autonomous Systems (1995), 14:199\u2013212.","journal-title":"Robotics and Autonomous Systems (1995)"},{"issue":"2\u20133","key":"10_CR18","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/BF00141150","volume":"3","author":"S. Hert","year":"1996","unstructured":"Hert S., Tiwari S., Lumelsky V., \u201cA terrain covering algorithm for an AUV,\u201d Auton. Robots, Vol.3, No.2\u20133 June\u2013July 1996, pp. 91\u2013119","journal-title":"Auton. Robots"},{"key":"10_CR19","volume-title":"Advanced Calculus","author":"W. Kaplan","year":"1984","unstructured":"Kaplan W., Advanced Calculus, 3\u2019rd Ed., Addison-Wesley, Reading, MA, 1984.","edition":"3\u2019rd Ed."},{"key":"10_CR20","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/0921-8890(91)90014-C","volume":"8","author":"Y. T. Kuipers Byun","year":"1981","unstructured":"Kuipers Byun Y. T., \u201cA robot exploration and mapping strategy based on a semantic hierarchy of spatial representations,\u201d Robotics and Autonomous Systems (1981), 8:47\u201363.","journal-title":"Robotics and Autonomous Systems (1981)"},{"key":"10_CR21","doi-asserted-by":"publisher","first-page":"665","DOI":"10.2307\/2371320","volume":"61","author":"R. Kershner","year":"1939","unstructured":"Kershner R., \u201cThe number of circles covering a set,\u201d Amer. J. Math. (1939), 61:665\u2013671.","journal-title":"Amer. J. Math. (1939)"},{"key":"10_CR22","doi-asserted-by":"crossref","unstructured":"LaValle S. M., Hutchinson S. A., \u201cEvaluating Motion Strategies under Nondeterministic or Probabilistic Uncertainties in Sensing and Control,\u201d Proc. of the 1996 IEEE Intl. Conference on Robotics and Automation, pp. 3034\u20133039.","DOI":"10.1109\/ROBOT.1996.509173"},{"key":"10_CR23","first-page":"353","volume-title":"Combinatorics, Paul Erd\u00f6s is Eighty, Part 2","author":"L. Lovasz","year":"1996","unstructured":"Lovasz L., \u201cRandom Walks on Graphs-a Survey,\u201d in: Combinatorics, Paul Erd\u00f6s is Eighty, Part 2 Ed. D. Miklos, V. T. Sos, T. Szony, Janos Bolyai Mathmatical Society, Budapest, 1996, Vol. 2, pp. 353\u2013398."},{"issue":"1","key":"10_CR24","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1214\/aop\/1176991894","volume":"16","author":"P. Matthews","year":"1988","unstructured":"Matthews P., \u201cCovering Problems for Brownian Motion On Spheres,\u201d The Annals of Probability, 1988, Vol. 16, No. 1, pp. 189\u2013199.","journal-title":"The Annals of Probability"},{"key":"10_CR25","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1017\/S0305004100033879","volume":"55","author":"C. St. J. A. Nash-Williams","year":"1959","unstructured":"Nash-Williams C. St. J. A., \u201cRandom walk and electric currents in networks,\u201d Proc. Camb. Phil. Soc., 55:181\u2013194, 1959.","journal-title":"Proc. Camb. Phil. Soc."},{"key":"10_CR26","volume-title":"New Trends in Discrete and Computational Geometry","year":"1993","unstructured":"Pach J. (Ed.), New Trends in Discrete and Computational Geometry, Springer-Verlag, Berlin Heidelberg 1993."},{"issue":"6","key":"10_CR27","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1163\/156855396X00228","volume":"10","author":"L. E. Parker","year":"1996","unstructured":"Parker L. E., \u201cOn the design of behavior-based multi-robot teams,\u201d Advanced Robotics, Vol. 10, No. 6, pp. 547\u2013578 (1996).","journal-title":"Advanced Robotics"},{"key":"10_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0871-6","volume-title":"Space-Filling Curves","author":"H. Sagan","year":"1994","unstructured":"Sagan H., Space-Filling Curves, Springer-Verlag, New York, 1994."},{"key":"10_CR29","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/978-1-4615-6281-8_16","volume-title":"Communications, Computation, Control, and Signal Processing: A Tribute to Thomas Kailath","author":"I. A. Wagner","year":"1997","unstructured":"Wagner I. A., Bruckstein A. M., \u201cCooperative Cleaners-a Study in AntRobotics,\u201d in A. Paulraj, V. Roychowdhury, C. D. Schaper-ed., Communications, Computation, Control, and Signal Processing: A Tribute to Thomas Kailath, Kluwer Academic Publishers, The Netherlands, 1997, pp. 289\u2013308."},{"key":"10_CR30","unstructured":"Wagner I. A., Lindenbaum M., Bruckstein A. M., \u201cOn-Line Graph Searching by a Smell-Oriented Vertex Process,\u201d Working notes of AAAI\u201997 Workshop on On-Line Search, July 28, 1997, Providence, Rhode Island, pp. 122\u2013125."},{"key":"10_CR31","unstructured":"Wagner I. A., Lindenbaum M., Bruckstein A. M., \u201cSmell as a Computational Resource-A Lesson We Can Learn from the Ant,\u201d Proceedings of the 4\u2019th Israeli Symposium on the Theory of Computing and Systems, Jerusalem, June 10\u201312, 1996."},{"issue":"4","key":"10_CR32","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1163\/156855396X00066","volume":"10","author":"H. Yaguchi","year":"1996","unstructured":"Yaguchi H., \u201cRobot introduction to cleaning work in the East Japan Railway Company,\u201d Advanced Robotics, Vol. 10, no. 4, pp. 403\u2013414 (1996).","journal-title":"Advanced Robotics"}],"container-title":["Lecture Notes in Computer Science","Randomization and Approximation Techniques in Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-49543-6_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T07:21:38Z","timestamp":1683876098000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-49543-6_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"ISBN":["9783540651420","9783540495437"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/3-540-49543-6_10","relation":{},"ISSN":["0302-9743"],"issn-type":[{"value":"0302-9743","type":"print"}],"subject":[],"published":{"date-parts":[[1998]]}}}