BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yifan Zhang (University of Ostrava\, VSB - Technical University of Ostrava) DTSTART:20260817T111500Z DTEND:20260817T120000Z DTSTAMP:20260612T023753Z UID:cam/105 DESCRIPTION:Title: Co verings of Complete Graphs by Small Cliques and Applications\nby Yifan Zhang (University of Ostrava\, VSB - Technical University of Ostrava) as part of CAM seminar\n\nLecture held in MV:L14.\n\nAbstract\nWhen solving p artial differential equations by fast Boundary Element Methods\, one is na turally led to large dense matrices whose computation must be split into m any smaller pieces for parallel execution on multiple cores. This motivate s a combinatorial load-balancing problem that can be modelled by covering the edges of a complete graph with small cliques\, each representing a com putational task.\nIn this talk\, I will discuss recent results on such cov erings of complete graphs by cliques of small order. The problem is closel y related to classical questions in design theory\, but is also driven by applications. If several clique sizes are permitted\, then minimising the number of blocks alone does not adequately describe the quality of a cover ing. We therefore study a refined criterion involving both the block count and the excess\, namely the number of edges covered more than once. I wil l present sharp results for coverings with 3- and 4-cliques\, and then tur n to the more difficult setting where 5-cliques are also allowed\, includi ng some open cases.\nMore broadly\, the talk illustrates how abstract comb inatorial structures can arise from concrete computational challenges\, an d how their study can feed back into the design of efficient parallel algo rithms.\n LOCATION:https://researchseminars.org/talk/cam/105/ END:VEVENT END:VCALENDAR