arXiv subjects

Tamas Lukovszki

Publications and source records attributed to Tamas Lukovszki.

3 recordsLinked to original sources

arXiv2020

Asynchronous Filling by Myopic Luminous Robots

We consider the problem of filling an unknown area represented by an arbitrary connected graph of $n$ vertices by mobile luminous robots. In this problem, the robots enter the graph one-by-one through a specific vertex, called the Door, and they eventually have to cover all vertices of the graph while avoiding collisions. The robots are anonymous and make decisions driven by the same local rule of behavior. They have limited persistent memory and limited visibility range. We investigate the Filling problem in the asynchronous model. We assume that the robots know an upper bound $Δ$ on the maximum degree of the graph before entering. We present an algorithm solving the asynchronous Filling problem with robots having $1$ hop visibility range, $O(\logΔ)$ bits of persistent storage, and $Δ+4$ colors, including the color when the light is off. We analyze the algorithm in terms of asynchronous rounds, where a round means the smallest time interval in which each robot, which has not yet finished the algorithm, has been activated at least once. We show that this algorithm needs $O(n^2)$ asynchronous rounds. Our analysis provides the first asymptotic upper bound on the running time in terms of asynchronous rounds. Then we show how the number of colors can be reduced to $O(1)$ at the cost of the running time. The algorithm with $1$ hop visibility range, $O(\log Δ)$ bits of persistent memory, and $O(1)$ colors needs $O(n^2\log Δ)$ rounds. We show how the running time can be improved by robots with a visibility range of $2$ hops, $O(\log Δ)$ bits of persistent memory, and $Δ+ 4$ colors (including the color when the light is off). We show that the algorithm needs $O(n)$ asynchronous rounds. Finally, we show how to extend our solution to the $k$-Door case, $k\geq 2$, by using $Δ+ k + 4$ colors, including the color when the light is off.

cs.DC↗

arXiv2017

Approximate and Incremental Network Function Placement

The virtualization and softwarization of modern computer networks introduces interesting new opportunities for a more flexible placement of network functions and middleboxes (firewalls, proxies, traffic optimizers, virtual switches, etc.). This paper studies approximation algorithms for the incremental deployment of a minimum number of middleboxes at optimal locations, such that capacity constraints at the middleboxes and length constraints on the communication routes are respected. Our main contribution is a new, purely combinatorial and rigorous proof for the submodularity of the function maximizing the number of communication requests that can be served by a given set of middleboxes. Our proof allows us to devise a deterministic approximation algorithm which uses an augmenting path approach to compute the submodular function. This algorithm does not require any changes to the locations of existing middleboxes or the preemption of previously served communication pairs when additional middleboxes are deployed, previously accepted communication pairs just can be handed over to another middlebox. It is hence particularly attractive for incremental deployments.We prove that the achieved polynomial-time approximation bound is optimal, unless P = NP. This paper also initiates the study of a weighted problem variant, in which entire groups of nodes need to communicate via a middlebox (e.g., a multiplexer or a shared object), possibly at different rates. We present an LP relaxation and randomized rounding algorithm for this problem, leveraging an interesting connection to scheduling.

cs.NI↗

arXiv2015

Online Admission Control and Embedding of Service Chains

The virtualization and softwarization of modern computer networks enables the definition and fast deployment of novel network services called service chains: sequences of virtualized network functions (e.g., firewalls, caches, traffic optimizers) through which traffic is routed between source and destination. This paper attends to the problem of admitting and embedding a maximum number of service chains, i.e., a maximum number of source-destination pairs which are routed via a sequence of to-be-allocated, capacitated network functions. We consider an Online variant of this maximum Service Chain Embedding Problem, short OSCEP, where requests arrive over time, in a worst-case manner. Our main contribution is a deterministic O(log L)-competitive online algorithm, under the assumption that capacities are at least logarithmic in L. We show that this is asymptotically optimal within the class of deterministic and randomized online algorithms. We also explore lower bounds for offline approximation algorithms, and prove that the offline problem is APX-hard for unit capacities and small L > 2, and even Poly-APX-hard in general, when there is no bound on L. These approximation lower bounds may be of independent interest, as they also extend to other problems such as Virtual Circuit Routing. Finally, we present an exact algorithm based on 0-1 programming, implying that the general offline SCEP is in NP and by the above hardness results it is NP-complete for constant L.

cs.NI↗