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View is a labeled directed graph containing all information about the network that a party can learn by exchanging messages with its neighbors. View can be used to solve distributed problems on an anonymous network (i.e., a network that does not guarantee that every party has a unique identifier). This paper presents an algorithm that constructs views in a compressed form on an anonymous n-party network...
It is well known that reasoning with AI temporal projection problems is difficult. Determining the Possible Truth problem, a basic temporal projection decision problem, in the so-called Simple Event System remains NP-complete. In this paper, two types of constraints, on the graph-theoretic representation of the cause-and-effect relationships between events and on the partial orders of events, are...
We study the complexity of finding extreme pure Nash equilibria in symmetric network congestion games and analyse how it depends on the graph topology and the number of users. In our context best and worst equilibria are those with minimum respectively maximum total latency. We establish that both problems can be solved by a Greedy algorithm with a suitable tie breaking rule on parallel links. On...
With economic constraints and limited routing capability, the structure of an access network is typically a "fat tree", where the terminal has to relay the traffic from another terminal of the same or higher level. New graph theory problems naturally arise from such features of access network models, different from those targeted towards survivable backbone (mesh) networks. We model the...
Let d = d(n) be the minimum d such that for every sequence of n subsets F1, F2, . . . , Fn of {1, 2, . . . , n} there exist n points P1, P2, . . . , Pn and n hyperplanes H1, H2 .... , Hn in Rd such that Pj lies in the positive side of Hi iff j ∈ Fi. Then n/32 ≤ d(n) ≤ (1/2 + 0(1)) ?? n. This implies that the probabilistic unbounded-error 2-way complexity of almost all the Boolean functions of 2p variables...
We give an algorithm to construct a cell decomposition of Rd, including adjacency information, defined by any given set of rational polynomials in d variables. The algorithm runs in single exponential parallel time, and in NC for fixed d. The algorithm extends a recent algorithm of Ben-Or, Kozen, and Reif for deciding the theory of real closed fields.
We consider the game of Checkers generalized to an N × N board. Although certain properties of positions are efficiently computable (e.g., can Black jump all of White's pieces in a single move?), the general question, given a position, of whether a specified player can force a win against best play by his opponent, is shown to be PSPACE-hard. Under certain reasonable assumptions about the "drawing...
This study may be viewed from the more general context of a theory of computational problems. An environment E= 〈L,D〉 consists of a class of structures D and a language L for D. A problem in E is a pair of sets of formulas P = 〈Π|Γ〉, with problem predicate Π. Let Ereal = 〈Lreal,{R}〉 and Elin = 〈Llin,Dlin〉 where R are the reals, Dlin is the class of totally ordered structures, Lreal and Llin are the...
We investigate the size of sets of computable functions using category-theoretic methods (in the sense of the Baire Category theorem). Constructive definitions of no-where dense and meagre set are given and applied to several problems. In particular we apply it to subrecursive degree structures and to a comparison of the power of deterministic and nondeterministic time bounded oracle machines.
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