69 research outputs found
A simpler and more efficient algorithm for the next-to-shortest path problem
Given an undirected graph with positive edge lengths and two
vertices and , the next-to-shortest path problem is to find an -path
which length is minimum amongst all -paths strictly longer than the
shortest path length. In this paper we show that the problem can be solved in
linear time if the distances from and to all other vertices are given.
Particularly our new algorithm runs in time for general
graphs, which improves the previous result of time for sparse
graphs, and takes only linear time for unweighted graphs, planar graphs, and
graphs with positive integer edge lengths.Comment: Partial result appeared in COCOA201
Dynamic Approximate Vertex Cover and Maximum Matching
We consider the problem of maintaining a large matching or a small vertex cover in a dynamically changing graph. Each update to the graph is either an edge deletion or an edge insertion. We give the first randomized data structure that simultaneously achieves a constant approximation factor and handles a sequence of k updates in k. polylog(n) time. Previous data structures require a polynomial amount of computation per update.
The starting point of our construction is a distributed algorithm of Parnas and Ron (Theor. Comput. Sci. 2007), which they designed for their sublinear-time approximation algorithm for the vertex cover size. This leads us to wonder whether there are other connections between sublinear algorithms and dynamic data structures.National Science Foundation (U.S.) (Grant 0732334)National Science Foundation (U.S.) (Grant 0728645)Marie Curie International (Reintegration Grant PIRG03-GA-2008-231077)Israel Science Foundation (Grant 1147/09)Israel Science Foundation (Grant 1675/09
Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs
A (1 + eps)-approximate distance oracle for a graph is a data structure that
supports approximate point-to-point shortest-path-distance queries. The most
relevant measures for a distance-oracle construction are: space, query time,
and preprocessing time. There are strong distance-oracle constructions known
for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs
(Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n)
space for n-node graphs. We argue that a very low space requirement is
essential. Since modern computer architectures involve hierarchical memory
(caches, primary memory, secondary memory), a high memory requirement in effect
may greatly increase the actual running time. Moreover, we would like data
structures that can be deployed on small mobile devices, such as handhelds,
which have relatively small primary memory. In this paper, for planar graphs,
bounded-genus graphs, and minor-excluded graphs we give distance-oracle
constructions that require only O(n) space. The big O hides only a fixed
constant, independent of \epsilon and independent of genus or size of an
excluded minor. The preprocessing times for our distance oracle are also faster
than those for the previously known constructions. For planar graphs, the
preprocessing time is O(n lg^2 n). However, our constructions have slower query
times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our
linear-space results, we can in fact ensure, for any delta > 0, that the space
required is only 1 + delta times the space required just to represent the graph
itself
Antichain Algorithms for Finite Automata
We present a general theory that exploits simulation relations on transition systems to obtain antichain algorithms for solving the reachability and repeated reachability problems. Antichains are more succinct than the sets of states manipulated by the traditional fixpoint algorithms. The theory justifies the correctness of the antichain algorithms, and applications such as the universality problem for finite automata illustrate efficiency improvements. Finally, we show that new and provably better antichain algorithms can be obtained for the emptiness problem of alternating automata over finite and infinite words
Simulation Subsumption in Ramsey-Based Büchi Automata Universality and Inclusion Testing
International audienc
A model-based approach for multiple QoS in scheduling: from models to implementation
Meeting multiple Quality of Service (QoS) requirements is an important factor in the success of complex software systems. This paper presents an automated, model-based scheduler synthesis approach for scheduling application software tasks to meet multiple QoS requirements. As a first step, it shows how designers can meet deadlock-freedom and timeliness requirements, in a manner that (i) does not over-provision resources, (ii) does not require architectural changes to the system, and that (iii) leaves enough degrees of freedom to pursue further properties. A major benefit of our synthesis methodology is that it increases traceability, by linking each scheduling constraint with a specific pair of QoS property and underlying platform execution model, so as to facilitate the validation of the scheduling constraints and the understanding of the overall system behaviour, required to meet further QoS properties.
The paper shows how the methodology is applied in practice and also presents a prototype implementation infrastructure for executing an application on top of common operating systems, without requiring modifications of the latter
Towards a Formal Concept Analysis Approach to Exploring Communities on the World Wide Web
Model-Based Verification, Optimization, Synthesis and Performance Evaluation of Real-Time Systems
International audienceThis article aims at providing a concise and precise Travellers Guide, Phrase Book or Reference Manual to the timed automata modeling formalism introduced by Alur and Dill [8, 9]. The paper gives comprehensive definitions of timed automata, priced (or weighted) timed automata, and timed games and highlights a number of results on associated decision problems related to model checking, equivalence checking, optimal scheduling, the existence of winning strategies, and then statistical model checking
Classifying Special Interest Groups in Web Graphs
We consider the problem of classifying special interest groups in web graphs. There is a secret society of blue vertices which link preferentially to each other. The other vertices, which are red, are unaware of the distinction between vertex colours and link to vertices arbitrarily. Each new vertex directs m edges towards the existing graph on joining it. The colour of the vertices is unknown. We give an algorithm which whp classifies all blue vertices, and all red vertices of high degree correctly. We also give an upper bound for the number of mis-classified red vertices
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