Stefan Dobrev

Searching for a black hole in arbitrary networks: optimal mobile agents protocols

Consider a networked environment, supporting mobile agents, where there is a black hole: a harmful host that disposes of visiting agents upon their arrival, leaving no observable trace of such a destruction. The black hole search problem is the one of assembling a team of asynchronous mobile agents, executing the same protocol and communicating by means of whiteboards, to successfully identify the location of the black hole; we are concerned with solutions that are generic (i.e., topology-independent). We establish tight bounds on the size of the team (i.e., the number of agents), and the cost (i.e., the number of moves) of a size-optimal solution protocol. These bounds depend on the a priori knowledge the agents have about the network, and on the consistency of the local labelings. In particular, we prove that: with topological ignorance Δ+1 agents are needed and suffice, and the cost is Θ(n2), where Δ is the maximal degree of a node and n is the number of nodes in the network; with topological ignorance but in presence of sense of direction only two agents suffice and the cost is Θ(n2); and with complete topological knowledge only two agents suffice and the cost is Θ(n log n). All the upper-bound proofs are constructive.

Multiple Agents RendezVous in a Ring in Spite of a Black Hole

The Rendezvous of anonymous mobile agents in a anonymous network is an intensively studied problem; it calls for k anonymous, mobile agents to gather in the same site. We study this problem when in the network there is a black hole: a stationary process located at a node that destroys any incoming agent without leaving any trace. The presence of the black hole makes it clearly impossible for all agents to rendezvous. So, the research concern is to determine how many agents can gather and under what conditions.

Measuring the problem-relevant information in input

We propose a new way of characterizing the complexity of online problems. Instead of measuring the degradation of the output quality caused by the ignorance of the future we choose to quantify the amount of additional global information needed for an online algorithm to solve the problem optimally. In our model, the algorithm cooperates with an oracle that can see the whole input. We define the advice complexity of the problem to be the minimal number of bits (normalized per input request, and minimized over all algorithm-oracle pairs) communicated by the algorithm to the oracle in order to solve the problem optimally. Hence, the advice complexity measures the amount of problem-relevant information contained in the input. We introduce two modes of communication between the algorithm and the oracle based on whether the oracle offers an advice spontaneously (helper) or on request (answerer). We analyze the Paging and DiffServ problems in terms of advice complexity and deliver upper and lower bounds in both communication modes; in the case of DiffServ problem in helper mode the bounds are tight.

Mobile Search for a Black Hole in an Anonymous Ring

We address the problem of mobile agents searching a ring network for a highly harmful item, a black hole, a stationary process destroying visiting agents upon their arrival. No observable trace of such a destruction will be evident. The location of the black hole is not known; the task is to unambiguously determine and report the location of the black hole. We answer some natural computational questions: How many agents are needed to locate the black hole in the ring ? How many suffice? What a-priori knowledge is required? as well as complexity questions, such as: With how many moves can the agents do it ? How long does it take ?

How much information about the future is needed

We propose a new way of characterizing the complexity of online problems. Instead of measuring the degradation of output quality caused by the ignorance of the future we choose to quantify the amount of additional global information needed for an online algorithm to solve the problem optimally. In our model, the algorithm cooperates with an oracle that can see the whole input. We define the advice complexity of the problem to be the minimal number of bits (normalized per input request, and minimized over all algorithm-oracle pairs) communicated between the algorithm and the oracle in order to solve the problem optimally. Hence, the advice complexity measures the amount of problem-relevant information contained in the input. We introduce two modes of communication between the algorithm and the oracle based on whether the oracle offers an advice spontaneously (helper) or on request (answerer). We analyze the Paging and DiffServ problems in terms of advice complexity and deliver tight bounds in both communication modes.

Searching for a black hole in arbitrary networks: optimal mobile agent protocols

Protecting agents from host attacks is a pressing security concern in networked environments supporting mobile agents. In this paper, we consider a black hole: a highly harmful host that disposes of visiting agents upon their arrival, leaving no observable trace of such a destruction. The task to identify the location of the harmful host is clearly dangerous for the searching agents. We study under what conditions and at what cost a team of autonomous asynchronous mobile agents can successfully accomplish this task; we are concerned with solutions that are generic (i.e., topology-independent). We study the size of the optimal solution (i.e., the minimum number of agents needed to locate the black hole), and the cost of the minimal solution (i.e., the number of moves performed by the agents executing a size-optimal solution protocol). We establish tight bounds on size and cost depending on the a priori knowledge the agents have about the network, and on the consistency of the local labellings. In particular, we prove that: with topological ignorance Δ + 1 agents are needed and suffice, and the cost is Θ(n2), where Δ is the maximal degree of a node and n is the number of the nodes in the network; with topological ignorance but in presence of sense of direction only two agents suffice and the cost is Θ(n2); and with complete topological knowledge only two agents suffice and the cost is Θ(n log n). All the upper-bound proofs are constructive.

Local algorithms for dominating and connected dominating sets of unit disk graphs with location aware nodes

Many protocols in ad-hoc networks use dominating and connected dominating sets, for example for broadcasting and routing. For large ad hoc networks the construction of such sets should be local in the sense that each node of the network should make decisions based only on the information obtained from nodes located a constant number of hops from it. In this paper we use the location awareness of the network, i.e. the knowledge of position of nodes in the plane to provide local, constant approximation, deterministic algorithms for the construction of dominating and connected dominating sets of a Unit Disk Graph (UDG). The size of the constructed set, in the case of the dominating set, is shown to be 5 times the optimal, while for the connected dominating set 7.453 + Ɛ the optimal, for any arbitrarily small Ɛ > 0. These are to our knowledge the first local algorithms whose time complexities and approximation bounds are independent of the size of the network.

Online graph exploration with advice

We study the problem of exploring an unknown undirected graph with non-negative edge weights. Starting at a distinguished initial vertex s, an agent must visit every vertex of the graph and return to s. Upon visiting a node, the agent learns all incident edges, their weights and endpoints. The goal is to find a tour with minimal cost of traversed edges. This variant of the exploration problem has been introduced by Kalyanasundaram and Pruhs in [18] and is known as a fixed graph scenario. There have been recent advances by Megow, Mehlhorn, and Schweitzer ([19]), however the main question whether there exists a deterministic algorithm with constant competitive ratio (w.r.t. to offline algorithm knowing the graph) working on all graphs and with arbitrary edge weights remains open. In this paper we study this problem in the context of advice complexity, investigating the tradeoff between the amount of advice available to the deterministic agent, and the quality of the solution. We show that Ω(n logn) bits of advice are necessary to achieve a competitive ratio of 1 (w.r.t. an optimal algorithm knowing the graph topology). Furthermore, we give a deterministic algorithm which uses O(n) bits of advice and achieves a constant competitive ratio on any graph with arbitrary weights. Finally, going back to the original problem, we prove a lower bound of 5/2−e for deterministic algorithms working with no advice, improving the best previous lower bound of 2−e of Miyazaki, Morimoto, and Okabe from [20]. In this case, significantly more elaborate technique was needed to achieve the result.

USING SCATTERED MOBILE AGENTS TO LOCATE A BLACK HOLE IN AN UN-ORIENTED RING WITH TOKENS

A black hole in a network is a highly harmful host that disposes of any incoming agents upon their arrival. Determining the location of a black hole in a ring network has been studied when each node is equipped with a whiteboard. Recently, the Black Hole Search problem was solved in a less demanding and less expensive token model with co-located agents. Whether the problem can be solved with scattered agents in a token model remains an open problem. In this paper, we show not only that a black hole can be located in a ring using tokens with scattered agents, but also that the problem is solvable even if the ring is un-oriented. More precisely, first we prove that the black hole search problem can be solved using only three scattered agents. We then show that, with K (K ⩾ 4) scattered agents, the black hole can be located in O(kn + n log n) moves. Moreover, when K (K ⩾ K) is a constant number, the move cost can be reduced to O(n log n), which is optimal. These results hold even if both agents and nodes are anonymous.

Local construction of planar spanners in unit disk graphs with irregular transmission ranges

We give an algorithm for constructing a connected spanning subgraphs(panner) of a wireless network modelled as a unit disk graph with nodes of irregular transmission ranges, whereby for some parameter 0 < r ≤ 1 the transmission range of a node includes the entire disk around the node of radius at least r and it does not include any node at distance more than one. The construction of a spanner is distributed and local in the sense that nodes use only information at their vicinity, moreover for a given integer k ≥ 2 each node needs only consider all the nodes at distance at most k hops from it. The resulting spanner has maximum degree at most 3 +