Author name cluster

E. Kranakis

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

4 papers

1 author row

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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TCS Journal 2011 Journal Article

Local 7-coloring for planar subgraphs of unit disk graphs

J. Czyzowicz
S. Dobrev
H. González-Aguilar
R. Kralovic
E. Kranakis
J. Opatrny
L. Stacho
J. Urrutia

We study the problem of computing locally a coloring of an arbitrary planar subgraph of a unit disk graph. Each vertex knows its coordinates in the plane and can communicate directly with all its neighbors within unit distance. Using this setting, first a simple algorithm is given whereby each vertex can compute its color in a 9-coloring of the planar graph using only information on the subgraph located within at most 9 hops away from it in the original unit disk graph. A more complicated algorithm is then presented whereby each vertex can compute its color in a 7-coloring of the planar graph using only information on the subgraph located within a constant number (201, to be exact) of hops away from it.

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TCS Journal 2009 Journal Article

Local edge colouring of Yao-like subgraphs of Unit Disk Graphs

J. Czyzowicz
S. Dobrev
E. Kranakis
J. Opatrny
J. Urrutia

The focus of the present paper is on providing a local deterministic algorithm for colouring the edges of Yao-like subgraphs of Unit Disk Graphs. These are geometric graphs such that for some positive integers l, k the following property holds at each node v: if we partition the unit circle centered at v into 2 k equally sized wedges then each wedge can contain at most l points different from v. We assume that the nodes are location aware, i. e. they know their Cartesian coordinates in the plane. The algorithm presented is local in the sense that each node can receive information emanating only from nodes which are at most a constant (depending on k and l, but not on the size of the graph) number of hops (measured in the original underlying Unit Disk Graph) away from it, and hence the algorithm terminates in a constant number of steps. The number of colours used is 2 k l + 1 and this is optimal for local algorithms (since the maximal degree is 2 k l and a colouring with 2 k l colours can only be constructed by a global algorithm), thus showing that in this class of graphs the price for locality is only one additional colour.

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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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