{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,14]],"date-time":"2025-06-14T12:40:02Z","timestamp":1749904802985,"version":"3.41.0"},"reference-count":45,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Parallel Comput."],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p>\n            We investigate routing in networks modeled as a set of stations sharing a channel. Packets are injected continually into stations. Each packet needs to be delivered to its destination station via the channel, possibly passing through relay stations. A station must be switched on to receive a packet successfully transmitted on the channel. Each station manages its on\/off schedule by a programmable mechanism. There is a bound on the number of stations that can be switched on simultaneously, called channel restraint. This system\u2019s component is motivated by constraints on the amount of power available for the system. Packet injection is governed by an adversary restricted by injection rate, which is an upper bound on the average number of packets that can be injected per round, and burstiness, which is a maximum number of packets that can be injected in a round. We present deterministic distributed routing algorithms and assess their worst-case performance. A routing algorithm knows the number of stations and the channel restraint but does not know the adversary. One of the algorithms maintains bounded queues in all stations for the maximum injection rate of\u00a01, subject only to the channel restraint of\u00a03. This restraint is provably optimal: obtaining the same throughput with channel restraint of 2 is impossible. We give universal routing algorithms, subject to the minimum channel restraint of\u00a02, that have latency polynomial in the number of stations\u00a0\n            <jats:italic>n<\/jats:italic>\n            , for each fixed adversary of injection rate less than\u00a01. An algorithm routes directly when each packet makes only one hop from the station into which it was injected straight to its destination. We present an algorithm routing indirectly with\n            <jats:italic>O(n)<\/jats:italic>\n            latency, for any fixed injection rate less than\u00a0\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\frac{1}{2}\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            , and another algorithm routing directly with\n            <jats:italic>O(n)<\/jats:italic>\n            latency, for any fixed injection rate less than\u00a0\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\frac{1}{3}\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            ; both algorithms with the channel restraint of\u00a02. An algorithm is\n            <jats:italic>k<\/jats:italic>\n            -channel-oblivious if at most\n            <jats:italic>k<\/jats:italic>\n            stations are switched on in a round, and, for each station, the rounds when it is switched on are determined in advance. We give a\n            <jats:italic>k<\/jats:italic>\n            -channel-oblivious algorithm routing indirectly with\n            <jats:italic>O(n)<\/jats:italic>\n            packet delay, for adversaries of injection rates less than\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\frac{k-1}{n-1}\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            , and show that no\n            <jats:italic>k<\/jats:italic>\n            -channel-oblivious algorithm exists that can keep queues bounded against adversaries with injection rates greater than\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\frac{k}{n}\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            . We give a\n            <jats:italic>k<\/jats:italic>\n            -channel-oblivious algorithm routing directly that has\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(O\\bigl (\\frac{n^2}{k}\\bigr)\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            latency, for adversaries with\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(O\\bigl (\\frac{k^2}{n^2}\\bigr)\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            injection rates. We develop a\n            <jats:italic>k<\/jats:italic>\n            -channel-oblivious algorithm routing directly that maintains bounded queues for the\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\frac{k(k-1)}{n(n-1)}\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            injection rate, and show that no\n            <jats:italic>k<\/jats:italic>\n            -channel-oblivious algorithm routing directly can keep queues bounded against adversaries with injection rates greater than\u00a0\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\frac{k(k-1)}{n(n-1)}\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            .\n          <\/jats:p>","DOI":"10.1145\/3730986","type":"journal-article","created":{"date-parts":[[2025,4,21]],"date-time":"2025-04-21T11:05:27Z","timestamp":1745233527000},"page":"1-39","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Energy Efficient Adversarial Routing in Shared Channels"],"prefix":"10.1145","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4884-941X","authenticated-orcid":false,"given":"Bogdan S.","family":"Chlebus","sequence":"first","affiliation":[{"name":"School of Computer and Cyber Sciences, Augusta University, Augusta, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0327-896X","authenticated-orcid":false,"given":"Elijah","family":"Hradovich","sequence":"additional","affiliation":[{"name":"Faculty of Fundamental Problems of Technology, Wroclaw University of Technology, Wroclaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1908-9458","authenticated-orcid":false,"given":"Tomasz","family":"Jurdzinski","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Wroclaw University, Wroclaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3141-8712","authenticated-orcid":false,"given":"Marek","family":"Klonowski","sequence":"additional","affiliation":[{"name":"Faculty of Fundamental Problems of Technology, Wroclaw University of Technology, Wroclaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1316-7788","authenticated-orcid":false,"given":"Dariusz R.","family":"Kowalski","sequence":"additional","affiliation":[{"name":"School of Computer and Cyber Sciences, Augusta University, Augusta, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,6,14]]},"reference":[{"issue":"5","key":"e_1_3_1_2_2","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1145\/1735223.1735245","article-title":"Energy-efficient algorithms","volume":"53","author":"Albers Susanne","year":"2010","unstructured":"Susanne Albers. 2010. 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