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D. Krizanc

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2 papers

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TCS Journal 2020 Journal Article

Priority evacuation from a disk: The case of n ≥ 4

J. Czyzowicz
K. Georgiou
R. Killick
E. Kranakis
D. Krizanc
L. Narayanan
J. Opatrny
S. Shende

We introduce and study a new search-type problem with ( n + 1 )-robots on a disk. The searchers (robots) all start from the center of the disk, have unit speed, and can communicate wirelessly. The goal is for a distinguished robot (the queen) to reach and evacuate from an exit that is hidden on the perimeter of the disk in as little time as possible. The remaining n robots (servants) are there to facilitate the queen's objective and are not required to reach the hidden exit. We provide upper and lower bounds for the time required to evacuate the queen from a unit disk. Namely, we propose an algorithm specifying the trajectories of the robots which guarantees evacuation of the queen in time always better than 2 + 4 ( 2 − 1 ) π n for n ≥ 4 servants. We also demonstrate that for n ≥ 4 servants the queen cannot be evacuated in time less than 2 + π n + 2 n 2.

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I&C Journal 1994 Journal Article

Computing Boolean Functions on Anonymous Networks

E. Kranakis
D. Krizanc
J. Vandenberg

We study the bit-complexity of computing Boolean functions on anonymous networks. Let N be the number of nodes, δ the diameter, and d the maximal node degree of the network. For arbitrary, anonymous networks we give a general algorithm of polynomial bit complexity O(N 3 · δ · d 2 · log N) for computing any Boolean function which is computable on the network. This improves upon the previous best known algorithm, which was of exponential bit complexity O(d N 2 ). For symmetric functions on arbitrary networks we give an algorithm with bit complexity O(N 3· δ · d 2 · log2 N). This same algorithm is shown to have even lower bit complexity for a number of specific networks, for example tori, hypercubes, and random regular graphs. We also consider the class of distance regular unlabeled networks and show that on such networks symmetric functions can be computed efficiently in O(N · δ · d · log N) bits.

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