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On the Connection between Interval Size Functions and Path Counting ⋆
"... Abstract. We investigate the complexity of hard counting problems that belong to the class #P but have easy decision version; several wellknown problems such as #Perfect Matchings, #DNFSat share this property. We focus on classes of such problems which emerged through two disparate approaches: one t ..."
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Abstract. We investigate the complexity of hard counting problems that belong to the class #P but have easy decision version; several wellknown problems such as #Perfect Matchings, #DNFSat share this property. We focus on classes of such problems which emerged through two disparate approaches: one taken by Hemaspaandra et al. [1] who defined classes of functions that count the size of intervals of ordered strings, and one followed by Kiayias et al. [2] who defined the class TotP, consisting of functions that count the total number of paths of NP computations. We provide inclusion and separation relations between TotP and interval size counting classes, by means of new classes that we define in this work. Our results imply that many known #Pcomplete problems with easy decision are contained in the classes defined in [1]—but are unlikely to be complete for these classes under certain types of reductions. We also define a new class of interval size functions which strictly contains FP and is strictly contained in TotP under reasonable complexitytheoretic assumptions. We show that this new class contains some hard counting problems. 1
Almost optimal asynchronous rendezvous in infinite multidimensional grids
 IN: PROC. OF THE 24TH INT. SYMP. ON DISTRIBUTED COMPUTING (DISC). VOLUME 6343 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2010
"... Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ> 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δdimen ..."
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Cited by 17 (1 self)
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Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ> 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δdimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(d δ polylog d). This bound for the case of 2dgrids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(d δ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δdimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(d δ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δdimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O( ( d)), where r = min(r1, r2) and for r ≥ 1. r)δpolylog ( d r 1
Euler tour lockin problem in the rotorrouter model  I choose pointers and you choose port numbers
 IN DISC, VOLUME 5805 OF LNCS
, 2009
"... The rotorrouter model, also called the Propp machine, was first considered as a deterministic alternative to the random walk. It is known that the route in an undirected graph G = (V, E), where V = n and E = m, adopted by an agent controlled by the rotorrouter mechanism forms eventually an E ..."
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Cited by 8 (3 self)
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The rotorrouter model, also called the Propp machine, was first considered as a deterministic alternative to the random walk. It is known that the route in an undirected graph G = (V, E), where V = n and E = m, adopted by an agent controlled by the rotorrouter mechanism forms eventually an Euler tour based on arcs obtained via replacing each edge in G by two arcs with opposite direction. The process of ushering the agent to an Euler tour is referred to as the lockin problem. In recent work [11] Yanovski et al. proved that independently of the initial configuration of the rotorrouter mechanism in G the agent locksin in time bounded by 2mD, where D is the diameter of G. In this paper we examine the dependence of the lockin time on the initial configuration of the rotorrouter mechanism. The case study is performed in the form of a game between a player P intending to lockin the agent in an Euler tour as quickly as possible and its adversary A with the counter objective. First, we observe that in certain (easy) cases
SelfStabilizing Balancing Algorithm for ContainmentBased Trees
, 2012
"... Abstract—Containmentbased trees encompass various handy structures such as B+trees, Rtrees and Mtrees. They are widely used to build data indexes, rangequeryable overlays, publish/subscribe systems both in centralized and distributed contexts. In addition to their versatility, their balanced sh ..."
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Abstract—Containmentbased trees encompass various handy structures such as B+trees, Rtrees and Mtrees. They are widely used to build data indexes, rangequeryable overlays, publish/subscribe systems both in centralized and distributed contexts. In addition to their versatility, their balanced shape ensures an overall satisfactory performance. Recently, it has been shown that their distributed implementations can be faultresilient. However, this robustness is achieved at the cost of unbalancing the structure. While the structure remains correct in terms of searchability, its performance can be significantly decreased. In this paper, we propose a distributed selfstabilizing algorithm to balance containmentbased trees. Index Terms—selfstabilization, balancing algorithms, containmentbased trees I.
Periodic Metro Scheduling ⋆
"... Abstract. We introduce the Periodic Metro Scheduling (PMS) problem, which aims in generating a periodic timetable for a given set of routes and a given time period, in such a way that the minimum time distance between any two successive trains that pass from the same point of the network is maximize ..."
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Abstract. We introduce the Periodic Metro Scheduling (PMS) problem, which aims in generating a periodic timetable for a given set of routes and a given time period, in such a way that the minimum time distance between any two successive trains that pass from the same point of the network is maximized. This can be particularly useful in cases where trains use the same rail segment quite often, as happens in metropolitan rail networks. We present exact algorithms for PMS in chain and spider networks, and constant ratio approximation algorithms for ring networks and for a special class of tree networks. Some of our algorithms are based on a reduction to the Path Coloring problem, while others rely on techniques specially designed for the new problem.
On a Noncooperative Model for Wavelength Assignment in Multifiber Optical Networks
, 2008
"... We study path multicoloring games that describe situations in which selfish entities possess communication requests in a multifiber alloptical network. Each player is charged according to the maximum fiber multiplicity that her color (wavelength) choice incurs and the social cost is the maximum pla ..."
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We study path multicoloring games that describe situations in which selfish entities possess communication requests in a multifiber alloptical network. Each player is charged according to the maximum fiber multiplicity that her color (wavelength) choice incurs and the social cost is the maximum player cost. We investigate the price of anarchy of such games and provide two different upper bounds for general graphs— namely the number of wavelengths and the minimum length of a path of maximum disutility, over all worstcase Nash Equilibria—as well as matching lower bounds which hold even for trees; as a corollary we obtain that the price of anarchy in stars is exactly 2. We also prove constant bounds for the price of anarchy in chains and rings in which the number of wavelengths is relatively small compared to the load of the network; in the opposite case we show that the price of anarchy is unbounded.
Improved Periodic Data Retrieval in Asynchronous Rings with a Faulty Host
"... Abstract. The exploration problem has been extensively studied in unsafe networks containing malicious hosts of a highly harmful nature, called black holes, which completely destroy mobile agents that visit them. In a recent work, Královič and Miklík [SIROCCO 2010, LNCS 6058, pp. 157–167] considere ..."
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Abstract. The exploration problem has been extensively studied in unsafe networks containing malicious hosts of a highly harmful nature, called black holes, which completely destroy mobile agents that visit them. In a recent work, Královič and Miklík [SIROCCO 2010, LNCS 6058, pp. 157–167] considered various types of malicious host behavior in the context of the Periodic Data Retrieval problem in asynchronous ring networks with exactly one malicious host. In this problem, a team of initially colocated agents must report data from all safe nodes of the network to the homebase, infinitely often. The malicious host can choose whether to kill visiting agents or allow them to pass through (gray hole). In another variation of the model, the malicious host can, in addition, alter its whiteboard contents in order to deceive visiting agents. The goal is to design a protocol for Periodic Data Retrieval using as few agents as possible. In this paper, we present the first nontrivial lower bounds on the num
Maximum Request Satisfaction in WDM Rings: Algorithms and Experiments
"... We study the problem of satisfying a maximum number of communication requests in alloptical WDM rings in which the number of available wavelengths per fiber is limited. We investigate two variations of the problem: with or without prior routing of requests. We consider a number of new and existing a ..."
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We study the problem of satisfying a maximum number of communication requests in alloptical WDM rings in which the number of available wavelengths per fiber is limited. We investigate two variations of the problem: with or without prior routing of requests. We consider a number of new and existing algorithmic approaches for these two variations. We perform an experimental comparison of the resulting algorithms, with respect to: (a) the number of satisfied requests and (b) the running time. We end up with interesting observations that reveal merits and deficiencies of the algorithms in hand: • All algorithms almost always manage to satisfy many more requests than indicated by their worstcase analysis. • Some algorithms are considerably faster than others with comparable request satisfaction performance. In fact, there are simple, fast algorithms that achieve a competent number of satisfied requests. We anticipate that our results will prove useful in practice, especially in deciding which routing and wavelength assignment method to choose, taking into account the desired level of accuracy and the affordable time cost.
Results 1  10
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