Jara Uitto

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

Solving the ANTS Problem with Asynchronous Finite State Machines

Consider the Ants Nearby Treasure Search (ANTS) problem introduced by Feinerman, Korman, Lotker, and Sereni (PODC 2012), where n mobile agents, initially placed in a single cell of an infinite grid, collaboratively search for an adversarially hidden treasure. In this paper, the model of Feinerman et al. is adapted such that each agent is controlled by an asynchronous (randomized) finite state machine: they possess a constant-size memory and can locally communicate with each other through constant-size messages. Despite the restriction to constant-size memory, we show that their collaborative performance remains the same by presenting a distributed algorithm that matches a lower bound established by Feinerman et al. on the run-time of any ANTS algorithm.

A lower bound for the distributed Lovász local lemma

We show that any randomised Monte Carlo distributed algorithm for the Lovász local lemma requires Omega(log log n) communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the special case of d = O(1), where d is the maximum degree of the dependency graph. By prior work, there are distributed algorithms for the Lovász local lemma with a running time of O(log n) rounds in bounded-degree graphs, and the best lower bound before our work was Omega(log* n) rounds [Chung et al. 2014].

How Many Ants Does It Take to Find the Food

Consider the Ants Nearby Treasure Search (ANTS) problem, where n mobile agents, initially placed at the origin of an infinite grid, collaboratively search for an adversarially hidden treasure. The agents are controlled by deterministic/randomized finite or pushdown automata and are able to communicate with each other through constant-size messages. We show that the minimum number of agents required to solve the ANTS problem crucially depends on the computational capabilities of the agents as well as the timing parameters of the execution environment. We give lower and upper bounds for different scenarios.

Fault-Tolerant ANTS

In this paper, we study a variant of the Ants Nearby Treasure Search problem, where n mobile agents, controlled by finite automata, search collaboratively for a treasure hidden by an adversary. In our version of the model, the agents may fail at any time during the execution. We provide a distributed protocol that enables the agents to detect failures and recover from them, thereby providing robustness to the protocol. More precisely, we provide a protocol that allows the agents to locate the treasure in time \(\mathcal{O}(D + D^2/n + Df)\) where D is the distance to the treasure and \(f \in \mathcal{O}(n)\) is the maximum number of failures.

SpareEye: enhancing the safety of inattentionally blind smartphone users

Using mobile phones while walking for activities that require continuous focus on the screen, such as texting, has become more and more popular in the last years. To avoid colliding with obstacles, such as lampposts and pedestrians, focus has to be taken off the screen in regular intervals. In this paper we introduce SpareEye, an Android application that warns the smartphone user from obstacles in her way. We use only the camera of the phone and no special hardware, ensuring that it requires minimal effort from the user to use the application during everyday life. Experimental results show that we can detect obstacles with high accuracy, with only some false positives and few false negatives.

How many ants does it take to find the food

Consider the Ants Nearby Treasure Search (ANTS) problem, where n mobile agents, initially placed at the origin of an infinite grid, collaboratively search for an adversarially hidden treasure. The agents are controlled by deterministic/randomized finite or pushdown automata and are able to communicate with each other through constant-size messages. We show that the minimum number of agents required to solve the ANTS problem crucially depends on the computational capabilities of the agents as well as the timing parameters of the execution environment. We give lower and upper bounds for different scenarios.

Lower Bounds for the Capture Time: Linear, Quadratic, and Beyond

In the classical game of Cops and Robbers on graphs, the capture time is defined by the least number of moves needed to catch all robbers with the smallest amount of cops that suffice. While the case of one cop and one robber is well understood, it is an open question how long it takes for multiple cops to catch multiple robbers. We show that capturing

A Tight Lower Bound for the Capture Time of the Cops and Robbers Game.

\ell \in {\mathcal{O}}\leftn\right

Randomness vs. Time in Anonymous Networks

robbers can take