arXiv subjects

Vladan Majerech

Publications and source records attributed to Vladan Majerech.

5 recordsLinked to original sources

arXiv2022

100 prisoners and a lightbulb -- looking back

100 prisoners and a light bulb is a long standing mathematical puzzle. The problem was studied mostly in 2002 [5], 2003 [1], and 2004 [3]. Solutions in published articles had average number of visits above 3850, but best solutions on forums had (declared) average number of visits around 3500. I spent some time in 2007-2009 to optimize the communication strategy and I pushed the average number of visits below 3390, seems no new ideas appear after it. Recently I have met several people familiar with published papers from 2002-2003 but not knowing newer results. Even after 2009 several papers on the topic were published where the new results were not mentioned [4]. Whole book was written about the problem [2]. This is why I am writing this summary.

cs.DM↗

arXiv2020

Fast DecreaseKey Heaps with worst-case variants

In the paper "Fast Fibonacci heaps with worst case extensions", we have described heaps with both Meld-DecreaseKey and DecreaseKey interfaces, allowing operations with guaranteed worst-case asymptotically optimal times. The paper was intended to concentrate on the DecreaseKey interface, but it could be hard to separate the two described data structures without careful reading. The current paper's goal is not to invent a novel data structure, but to describe a rather easy DecreaseKey version in a hopefully readable form. The paper is intended not to require reference to other papers.

cs.DS↗

arXiv2019

Fast Fibonacci heaps with worst case extensions

We are concentrating on reducing overhead of heaps based on comparisons with optimal worstcase behaviour. The paper is inspired by Strict Fibonacci Heaps [1], where G. S. Brodal, G. Lagogiannis, and R. E. Tarjan implemented the heap with DecreaseKey and Meld interface in assymptotically optimal worst case times (based on key comparisons). In the paper [2], the ideas were elaborated and it was shown that the same asymptotical times could be achieved with a strategy loosing much less information from previous comparisons. There is big overhead with maintainance of violation lists in these heaps. We propose simple alternative reducing this overhead. It allows us to implement fast amortized Fibonacci heaps, where user could call some methods in variants guaranting worst case time. If he does so, the heaps are not guaranted to be Fibonacci until an amortized version of a method is called. Of course we could call worst case versions all the time, but as there is an overhead with the guarantee, calling amortized versions is prefered choice if we are not concentrated on complexity of the separate operation. We have shown, we could implement full DecreaseKey-Meld interface, but Meld interface is not natural for these heaps, so if Meld is not needed, much simpler implementation suffices. As I don't know application requiring Meld, we would concentrate on noMeld variant, but we will show the changes could be applied on Meld including variant as well. The papers [1], [2] shown the heaps could be implemented on pointer machine model. For fast practical implementations we would rather use arrays. Our goal is to reduce number of pointer manipulations. Maintainance of ranks by pointers to rank lists would be unnecessary overhead.

cs.DS↗

arXiv2019

Information carefull worstcase DecreaseKey heaps with simple nonMeld variant

We analyze priority queues including DecreaseKey method in its interface. The paper is inspired by Strict Fibonacci Heaps [2], where G. S. Brodal, G. Lagogiannis, and R. E. Tarjan implemented the heap with DecreaseKey and Meld interface in assymptotically optimal worst case times (based on key comparisons). At the end of the paper there are mentioned possible variants of other structural properties an violations than they have used in the analysis. In the main variant a lot of information is wasted during violation reduction steps. Our goal is to concentrate on other variants and to invent natural strategy not losing that much in the information value. In other words we try to choose among them one which corresponds to superexpensive comparision principle as much as possible. The principle was described in [5] of myself, but after publication I have found these ideas in [4] of H. Kaplan, R. E. Tarjan, and U. Zwick.

cs.DS↗

arXiv2019

Padovan heaps

We analyze priority queues of Fibonacci family. The paper is inspired by Violation heap [1], where A. Elmasry saves one pointer in representation of Fibonacci heap nodes while achieving the same amortized bounds as Fibonacci heaps [2] of M. L. Fredman and R. E. Tarjan. Unfortunately author forces the heaps to be wide, what goes against optimal heap principles. Our goal is to achieve the same result, but with much narrower heaps. We follow the principle of superexpensive comparison so we try to remember results of all comparisons and never compare elements that cannot be minimal. We delay comparisons as long as possible. Actually I have always want to share superexpensive comparison principle ideas, discovery of Padovan heaps allowed me to do so. Of course saving one pointer is not that big goal, but I hope the presented reasoning and amortized analysis of the resulting heaps is worth a publication.

cs.DS↗