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In this work, we derive a factor 66-approximation algorithm for<jats:sc>Tracking Paths<\/jats:sc>in weighted graphs and a factor 4-approximation algorithm if the input is unweighted. This is the first constant factor approximation for this problem. While doing so, we also study approximation of the closely related<jats:italic>r<\/jats:italic><jats:sc>-Fault Tolerant Feedback Vertex Set<\/jats:sc>problem. There, for a fixed integer\u00a0<jats:italic>r<\/jats:italic>and a given vertex-weighted graph<jats:italic>G<\/jats:italic>, the task is to find a minimum weight set of vertices intersecting every cycle of\u00a0<jats:italic>G<\/jats:italic>in at least\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$r+1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>r<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>vertices. We give a factor<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal {O}(r^2)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>O<\/mml:mi><mml:mo>(<\/mml:mo><mml:msup><mml:mi>r<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>approximation algorithm for<jats:italic>r<\/jats:italic><jats:sc>-Fault Tolerant Feedback Vertex Set<\/jats:sc>if<jats:italic>r<\/jats:italic>is a constant.<\/jats:p>","DOI":"10.1007\/978-3-030-92702-8_2","type":"book-chapter","created":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T06:00:24Z","timestamp":1641016824000},"page":"23-38","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Constant Factor Approximation for\u00a0Tracking Paths and\u00a0Fault Tolerant Feedback Vertex Set"],"prefix":"10.1007","author":[{"given":"V\u00e1clav","family":"Bla\u017eej","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pratibha","family":"Choudhary","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Du\u0161an","family":"Knop","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan Maty\u00e1\u0161","family":"K\u0159i\u0161t\u2019an","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ond\u0159ej","family":"Such\u00fd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tom\u00e1\u0161","family":"Valla","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,1,1]]},"reference":[{"key":"2_CR1","unstructured":"Abid, A., Khan, F., Hayat, M., Khan, W.: Real-time object tracking in wireless sensor network. 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