{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:06:31Z","timestamp":1759147591257,"version":"3.41.0"},"reference-count":28,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2018,6,28]],"date-time":"2018-06-28T00:00:00Z","timestamp":1530144000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"SRIC, IIT Roorkee"},{"name":"SERB, Govt. of India","award":["ECR\/2016\/001921"],"award-info":[{"award-number":["ECR\/2016\/001921"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Des. Autom. Electron. Syst."],"published-print":{"date-parts":[[2018,7,31]]},"abstract":"<jats:p>\n            Recent studies in algorithmic microfluidics have led to the development of several techniques for automated solution preparation using droplet-based digital microfluidic (DMF) biochips. A major challenge in this direction is to produce a mixture of several reactants with a desired ratio while optimizing reactant cost and preparation time. The sequence of mix-split operations that are to be performed on the droplets is usually represented as a mixing tree (or graph). In this article, we present an efficient mixing algorithm, namely, Mixing Tree with Common Subtrees (\n            <jats:italic>MTCS<\/jats:italic>\n            ), for preparing single-target mixtures.\n            <jats:italic>MTCS<\/jats:italic>\n            attempts to best utilize intermediate droplets, which were otherwise wasted, and uses morphing based on permutation of leaf nodes to further reduce the graph size. The technique can be generalized to produce multitarget ratios, and we present another algorithm, namely, Multiple Target Ratios (\n            <jats:italic>MTR<\/jats:italic>\n            ). Additionally, in order to enhance the output load, we also propose an algorithm for droplet streaming called Multitarget Multidemand (\n            <jats:italic>MTMD<\/jats:italic>\n            ). Simulation results on a large set of target ratios show that\n            <jats:italic>MTCS<\/jats:italic>\n            can reduce the mean values of the total number of mix-split steps (\n            <jats:italic>T<\/jats:italic>\n            <jats:sub>\n              <jats:italic>ms<\/jats:italic>\n            <\/jats:sub>\n            ) and waste droplets (\n            <jats:italic>W<\/jats:italic>\n            ) by 16% and 29% over\n            <jats:italic>Min-Mix<\/jats:italic>\n            (Thies et al. 2008) and by 22% and 34% over\n            <jats:italic>RMA<\/jats:italic>\n            (Roy et al. 2015), respectively. Experimental results also suggest that\n            <jats:italic>MTR<\/jats:italic>\n            can reduce the average values of\n            <jats:italic>T<\/jats:italic>\n            <jats:sub>\n              <jats:italic>ms<\/jats:italic>\n            <\/jats:sub>\n            and\n            <jats:italic>W<\/jats:italic>\n            by 23% and 44% over the repeated version of\n            <jats:italic>Min-Mix<\/jats:italic>\n            , by 30% and 49% over the repeated version of\n            <jats:italic>RMA<\/jats:italic>\n            , and by 9% and 22% over the repeated-version of\n            <jats:italic>MTCS<\/jats:italic>\n            , respectively. It is observed that\n            <jats:italic>MTMD<\/jats:italic>\n            can reduce the mean values of\n            <jats:italic>T<\/jats:italic>\n            <jats:sub>\n              <jats:italic>ms<\/jats:italic>\n            <\/jats:sub>\n            and\n            <jats:italic>W<\/jats:italic>\n            by 64% and 85%, respectively, over\n            <jats:italic>MTR<\/jats:italic>\n            . Thus, the proposed multitarget techniques\n            <jats:italic>MTR<\/jats:italic>\n            and\n            <jats:italic>MTMD<\/jats:italic>\n            provide efficient solutions to multidemand, multitarget mixture preparationon a DMF platform.\n          <\/jats:p>","DOI":"10.1145\/3200903","type":"journal-article","created":{"date-parts":[[2018,6,28]],"date-time":"2018-06-28T16:38:11Z","timestamp":1530203891000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Demand-Driven Single- and Multitarget Mixture Preparation Using Digital Microfluidic Biochips"],"prefix":"10.1145","volume":"23","author":[{"family":"Shalu","sequence":"first","affiliation":[{"name":"Indian Institute of Technology Roorkee, Roorkee, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Srijan","family":"Kumar","sequence":"additional","affiliation":[{"name":"Stanford University, California, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ananya","family":"Singla","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Roorkee, Roorkee, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sudip","family":"Roy","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Roorkee, Roorkee, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krishnendu","family":"Chakrabarty","sequence":"additional","affiliation":[{"name":"Duke University, Durham, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Partha P.","family":"Chakrabarti","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Kharagpur, Kharagpur, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bhargab B.","family":"Bhattacharya","sequence":"additional","affiliation":[{"name":"Indian Statistical Institute Kolkata, Kolkata, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,6,28]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_2_1_1","DOI":"10.1186\/1754-1611-4-13"},{"doi-asserted-by":"publisher","key":"e_1_2_2_2_1","DOI":"10.1109\/TCAD.2016.2585622"},{"doi-asserted-by":"crossref","unstructured":"K. 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