Christoph Ambühl

Efficient Algorithms for Low-Energy Bounded-Hop Broadcast in Ad-Hoc Wireless Networks

The paper studies the problem of computing a minimal energy cost range assignment in a ad-hoc wireless network which allows a station s to perform a broadcast operation in at most h hops. The general version of the problem (i.e., when transmission costs are arbitrary) is known to be log-APX hard even for h = 2. The current paper considers the well-studied real case in which n stations are located on the plane and the cost to transmit from station i to station j is proportional to the α-th power of the distance between station i and j, where α is any positive constant. A polynomial-time algorithm is presented for finding an optimal range assignment to perform a 2-hop broadcast from a given source station. The algorithm relies on dynamic programming and operates in (worst-case) time O(n 7 ). Then, a polynomial-time approximation scheme (PTAS) is provided for the above problem for any fixed h > 1. For fixed h > 1 and ∈ > 0, the PTAS has time complexity O(n μ ) where μ = O((α2 α h α /∈)α h ).

Computing Largest Common Point Sets under Approximate Congruence

The problem of computing a largest common point set (LCP) between two point sets under Ɛ-congruence with the bottleneck matching metric has recently been a subject of extensive study. Although polynomial time solutions are known for the planar case and for restricted sets of transformations and metrics (like translations and the Hausdorff-metric under L∞-norm), no complexity results are formally known for the general problem. In this paper we give polynomial time algorithms for this problem under different classes of transformations and metrics for any fixed dimension, and establish NP-hardness for unbounded dimensions. Any solution to this (or related) problem, especially in higher dimensions, is generally believed to involve implementation difficulties because they rely on the computation of intersections between algebraic surfaces. We show that (contrary to intuitive expectations) this problem can be solved under a rational arithmetic model in a straightforward manner if the set of transformations is extended to general affine transformations under the L∞-norm (difficulty of this problem is generally expected to be in the order: translations < rotation < isometry < more general). To the best of our knowledge this is also the first paper which deals with the LCP-problem under such a general class of transformations.

The range assignment problem in non-homogeneous static ad-hoc networks

Summary form only given. We introduce the weighted version of the range assignment problem in which the cost a station s pays to transmit to another station depends on the distance between the stations and on the energy cost of station s. Most of the algorithm results for the unweighted range assignment problem can not be applied to the weighted version. We thus provide a set of algorithmic results for this version and discuss some interesting related open questions.

Energy consumption in radio networks: Selfish agents and rewarding mechanisms

We consider the range assignment problem in ad-hoc wireless networks in the context of selfish agents: a network manager aims in assigning transmission ranges to the stations so to achieve a suitable network with a minimal overall energy; stations are not directly controlled by the manager and may refuse to transmit with a certain transmission range because this results in a power consumption proportional to that range.

On-line scheduling to minimize max flow time: an optimal preemptive algorithm

We investigate the maximum flow time minimization problem of on-line scheduling jobs on m identical parallel machines. When preemption is allowed, we derive an optimal algorithm with competitive ratio 2-1/m. When preemption is not allowed and m=2, we show that the First In First Out heuristic achieves the best possible competitive ratio.

Offline List Update is NP-Hard

In the offline list update problem, we maintain an unsorted linear list used as a dictionary. Accessing the item at position i in the list costs i units. In order to reduce access cost, we are allowed to update the list at any time by transposing consecutive items at a cost of one unit. Given a sequence σ of requests one has to serve in turn, we are interested in the minimal cost needed to serve all requests. Little is known about this problem. The best algorithm so far needs exponential time in the number of items in the list. We show that there is no polynomial algorithm unless P = NP.

A new lower bound for the list update problem in the partial cost model

The optimal competitive ratio for a randomized online list update algorithm is known to be at least 1.5 and at most 1.6, but the remaining gap is not yet closed. We present a new lower bound of 1.50084 for the partial cost model. The construction is based on game trees with incomplete information, which seem to be generally useful for the competitive analysis of online algorithms. 2001 Elsevier Science B.V.

The Clique Problem in Intersection Graphs of Ellipses and Triangles

AbstractIntersection graphs of disks and of line segments, respectively, have been well studied, because of both practical applications and theoretically interesting properties of these graphs. Despite partial results, the complexity status of the Clique problem for these two graph classes is still open. Here, we consider the Clique problem for intersection graphs of ellipses, which, in a sense, interpolate between disks and line segments, and show that the problem is APX-hard in that case. Moreover, this holds even if for all ellipses, the ratio of the larger over the smaller radius is some prescribed number. Furthermore, the reduction immediately carries over to intersection graphs of triangles. To our knowledge, this is the first hardness result for the Clique problem in intersection graphs of convex objects with finite description complexity. We also describe a simple approximation algorithm for the case of ellipses for which the ratio of radii is bounded.

On the approximability of the range assignment problem on radio networks in presence of selfish agents

We consider the range assignment problem in ad-hoc wireless networks in the context of selfish agents: A network manager aims to assigning transmission ranges to the stations in order to achieve strong connectivity of the network within a minimal overallpower consumption. Station is not directly controlled by the manager and may refuse to transmit with a certain transmission range because it might be costly in terms of power consumption.We investigate the existence of payment schemes which induce the stations to follow the decisions of a network manager in computing a range assignment, that is, truthful mechanisms for the range assignment problem. We provide both positive and negative results on the existence of truthful VCG-based mechanisms for this NP-hard problem. We prove that (i) in general, every polynomial-time truthful VCG-based mechanism computes a solution of cost far-off the optimum, unless P = NP and (ii) there exists a polynomial-time truthful VCG-based mechanism achieving constant approximation for practically relevant, still NP-hard versions, i.e., the metric and the well-spread case.

Optimal Projective Algorithms for the List Update Problem

The list update problem is a classical online problem, with an optimal competitive ratio that is still open, somewhere between 1.5 and 1.6. An algorithm with competitive ratio 1.6, the smallest known to date, is COMB, a randomized combination of BIT and TIMESTAMP. This and many other known algorithms, like MTF, are projective in the sense that they can be defined by only looking at any pair of list items at a time. Projectivity simplifies both the description of the algorithm and its analysis, and so far seems to be the only way to define a good online algorithm for lists of arbitrary length. In this paper we characterize all projective list update algorithms and show their competitive ratio is never smaller than 1.6. Therefore, COMB is a best possible projective algorithm, and any better algorithm, if it exists, would need a non-projective approach.