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PRODID:-//University of Liverpool Computer Science Seminar System//v2//EN
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DTSTAMP:20260922T060802Z
UID:Seminar-EcCo-602@lxserverM.csc.liv.ac.uk
ORGANIZER:CN=Nicos 	Protopapas:MAILTO:N.Protopapas@liverpool.ac.uk
DTSTART:20190522T130000
DTEND:20190522T140000
SUMMARY:Economics and Computation Series
DESCRIPTION:Nan Zhi: Ultimate greedy approximation of independent sets in subcubic graphs\n\nWe study the approximability of the maximum size independent set (MIS) problem in bounded degree graphs.  This is one of the most classic and widely studied NP-hard optimization problems. It is known for its inherent hardness of approximation.\n\nWe focus on the well known minimum degree greedy algorithm for this problem. This algorithm iteratively chooses a minimum degree vertex in the graph, adds it to the solution and removes its neighbors, until the remaining graph is empty. The approximation ratios of this algorithm have been very widely studied, where it is augmented with an advice that tells the greedy which minimum degree vertex to choose if it is not unique.\n\nOur main contribution is a new mathematical theory for the design of such greedy algorithms with efficiently computable advice and for the analysis of their approximation ratios. With this new theory we obtain the ultimate approximation ratio of 5/4 for greedy on graphs with maximum degree 3, which completely solves the open problem from the paper by Halldorsson and Yoshihara (1995). Our algorithm is the fastest currently known algorithm with this approximation ratio on such graphs. We also obtain a simple and short proof of the (D+2)/3-approximation ratio of any greedy on graphs with maximum degree D, the result proved previously by Halldorsson and Radhakrishnan (1994). We almost match this ratio by showing a lower bound of (D+1)/3 on the ratio of any greedy algorithm that can use any advice. We apply our new algorithm to the minimum vertex cover problem on graphs with maximum degree 3 to obtain a substantially faster 6/5-approximation algorithm than the one currently known.\n\nWe complement our positive, upper bound results with negative, lower bound results which prove that the problem of designing good advice for greedy is computationally hard \nand even hard to approximate on various classes of graphs. These results significantly improve on such previously known hardness results. Moreover, these results suggest that obtaining the upper bound results on the design and analysis of greedy advice is non-trivial.\n\nIn my talk I will present a short overview of our lower bounds results and then I will focus on our ultimate greedy 5/4-approximation algorithm.\n\nThis is joint work with Piotr Krysta and Mathieu Mari.\n\nhttps://www.csc.liv.ac.uk/research/seminars/abstract.php?id=602
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