Related papers: Deterministic Graph Exploration with Advice
Let $G$ be an edge-weighted directed graph with $n$ vertices embedded on an orientable surface of genus $g$. We describe a simple deterministic lexicographic perturbation scheme that guarantees uniqueness of minimum-cost flows and shortest…
Given an undirected $n$-vertex planar graph $G=(V,E,\omega)$ with non-negative edge weight function $\omega:E\rightarrow \mathbb R$ and given an assigned label to each vertex, a vertex-labeled distance oracle is a data structure which for…
There is substantial literature dealing with fixed parameter algorithms for the dominating set problem on various families of graphs. In this paper, we give a $k^{O(dk)} n$ time algorithm for finding a dominating set of size at most $k$ in…
We consider the k-server problem under the advice model of computation when the underlying metric space is sparse. On one side, we show that an advice of size {\Omega}(n) is required to obtain a 1-competitive algorithm for sequences of size…
We consider coloring problems in the distributed message-passing setting. The previously-known deterministic algorithms for edge-coloring employed at least (2Delta - 1) colors, even though any graph admits an edge-coloring with Delta + 1…
We consider a modified random walk which uses unvisited edges whenever possible, and makes a simple random walk otherwise. We call such a walk an edge-process. We assume there is a rule A, which tells the walk which unvisited edge to use…
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…
We consider a graph observability problem: how many edge colors are needed for an unlabeled graph so that an agent, walking from node to node, can uniquely determine its location from just the observed color sequence of the walk?…
In this paper we study the fixed-parameter tractability of the problem of deciding whether a given temporal graph admits a temporal walk that visits all vertices (temporal exploration) or, in some problem variants, a certain subset of the…
In rendezvous, two agents traverse network edges in synchronous rounds and have to meet at some node. In treasure hunt, a single agent has to find a stationary target situated at an unknown node of the network. We study tradeoffs between…
We consider the problem of assigning appearing times to the edges of a digraph in order to maximize the (average) temporal reachability between pairs of nodes. Motivated by the application to public transit networks, where edges cannot be…
Recent papers have shown optimally-competitive on-line strategies for a robot traveling from a point $s$ to a point $t$ in certain unknown geometric environments. We consider the question: Having gained some partial information about the…
A temporal graph is a graph in which edges are assigned a time label. Two nodes u and v of a temporal graph are connected one to the other if there exists a path from u to v with increasing edge time labels. We consider the problem of…
Given a network of fixed size $n$ and an initial distribution of data, we derive sufficient connectivity conditions on a sequence of time-varying digraphs for (a) data collection and (b) data dissemination, within at most $(n-1)$…
We revisit once more the problem of designing an oracle for answering connectivity queries in undirected graphs in the presence of vertex failures. Specifically, given an undirected graph $G$ with $n$ vertices and $m$ edges and an integer…
We consider an online version of a longest path problem in an undirected and planar graph that is motivated by a location and routing problem occurring in the board game "Turn & Taxis". Path extensions have to be selected based on only…
We study the problem of estimating the number of defective items $d$ within a pile of $n$ elements up to a multiplicative factor of $\Delta>1$, using deterministic group testing algorithms. We bring lower and upper bounds on the number of…
We investigate the computational power of the deterministic single-agent model where the agent and each node are equipped with a limited amount of persistent memory. Tasks are formalized as decision problems on properties of input graphs,…
Consider a group of autonomous mobile computational entities, called agents, arbitrarily placed at some nodes of a dynamic but always connected ring. The agents neither have any knowledge about the size of the ring nor have a common notion…
Let $P$ be a set of $n$ points in the plane, where each point $p\in P$ has a transmission radius $r(p)>0$. The transmission graph defined by $P$ and the given radii, denoted by $\mathcal{G}_{\mathrm{tr}}(P)$, is the directed graph whose…