Online Algorithms for Multi-Level Aggregation

In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edge-weighted tree T, and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the TCP Acknowledgment Problem, while for trees of depth 2, it is equivalent to the Joint Replenishment Problem. Aggregation problem for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies, and in supply-chain management. The instances of MLAP associated with these applications are naturally online, in the sense that aggregation decisions need to be made without information about future requests. Constant-competitive online algorithms are known for MLAP with one or two levels. However, it has been open whether there exist constant competitive online algorithms for trees of depth more than 2. Addressing this open problem, we give the first constant competitive online algorithm for networks of arbitrary (fixed) number of levels. The competitive ratio is O(D^4 2^D), where D is the depth of T. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines. We also show several additional lower and upper bound results for some special cases of MLAP, including the Single-Phase variant and the case when the tree is a path

Online packet scheduling with bounded delay and lookahead

We study the online bounded-delay packet scheduling problem (Packet Scheduling), where packets of unit size arrive at a router over time and need to be transmitted over a network link. Each packet has two attributes: a non-negative weight and a deadline for its transmission. The objective is to maximize the total weight of the transmitted packets. This problem has been well studied in the literature; yet currently the best published upper bound is 1.828 [8],still quite far from the best lower bound ofφ≈1.618 [11, 2, 6].In the variant of Packet Scheduling with s-bounded instances, each packet can be scheduled in at most s consecutive slots, starting at its release time. The lower bound of φ applies even to the special case of 2-bounded instances, and a φ-competitive algorithm for 3-boundedinstances was given in [5]. Improving that result, and addressing a question posed by Goldwasser [9], we present a φ-competitive algorithm for 4-boundedinstances. We also study a variant of Packet Scheduling where an online algorithm has the additional power of1-lookahead, knowing at time t which packets will arrive at time t+ 1. For Packet Scheduling with 1-lookahead restricted to 2-bounded instances, we present an online algorithm with competitive ratio12(√13−1)≈1.303 and we prove a nearly tight lower boundof14(1 +√17)≈1.281. In fact, our lower bound result is more general: using only 2-boundedinstances, for any integer`≥0 we prove a lower bound of12(`+1)(1 +√5 + 8`+ 4`2) for online algorithms with`-look ahead, i.e., algorithms that at time t can see all packets arriving by time t+`. Finally, for non-restricted instances we show a lower bound of 1.25 for randomized algorithms with`-lookahead, for any`≥0

Comparison of safety and kinematic patterns of automated vehicles turning left in interaction with oncoming manually driven vehicles

Highly and fully automated driving has been under development for the past two decades in order to increase comfort, efficiency, and traffic safety. Particularly in the latter domain, experts agree on automated driving, especially in case of automated vehicles (AV) with SAE level 4 or higher, having the most promising effects. Automated driving is expected to decrease the number of seriously injured or even killed road usersto zero (Vision Zero). However, automated driving is still in an early stage of development and many AV tend to drive very carefully to avoid crashes. So, the goal is to make driving more efficient while maintaining the highest level of safety. In the project Digitaler Knoten 4.0 cooperative automated driving was assessed regarding efficiency and safety aspects. One of the use cases investigated was turning left with oncoming traffic at an urban intersection as this situation represents one of the most complex situations in urban areas yielding to crashes with—in many cases—serious consequences for the involved road users. At the Application Platform Intelligent Mobility (AIM) Research Intersection in Braunschweig, Germany, an SAE level 3 AV was turning left interacting with oncoming manually driven vehicles (MV). The performance of the AV was compared to MV executing the same manoeuvre. The recorded video-based trajectories of the respective AV as well as MV were analysed regarding the influence of situational factors (e.g. position of the vehicle in the queue and gap acceptance) and kinematic factors (e.g. speed and acceleration) on traffic safety. The similarities and differences between this specific AV and MV were identified yielding insight for further developing algorithms for more efficient driving while maintaining the same traffic safety level. For instance, it appears that the AV shows a very conservative left turning behaviour leading to very safe PET distributions in comparison to left turning MV

Comparison of safety and kinematic patterns of automated vehicles turning left in interaction with oncoming manually driven vehicles

Highly and fully automated driving has been under devel-opment for the past two decades in order to increase comfort, efficiency, and traffic safety. Particularly in the latter domain, experts agree on automated driving, especially in case of automated vehicles (AV) with SAE level 4 or higher, having the most promising effects. Automated driving is expected to decrease the number of seriously injured or even killed road users to zero (Vision Zero). However, automated driving is still in an early stage of development and many AV tend to drive very carefully to avoid crashes. So, the goal is to make driving more efficient while maintaining the highest level of safety. In the project “Digitaler Knoten 4.0” cooperative automated driving was assessed regarding ef-ficiency and safety aspects. One of the use cases investigated was turn-ing left with oncoming traffic at an urban intersection as this situation represents one of the most complex situations in urban areas yielding to crashes with—in many cases—serious consequences for the involved road users. At the Application Platform Intelligent Mobility (AIM) Re-search Intersection in Braunschweig, Germany, an SAE level 3 AV was turning left interacting with oncoming manually driven vehicles (MV). The performance of the AV was compared to MV executing the same manoeuvre. The recorded video-based trajectories of the respective AV as well as MV were analysed regarding the influence of situational factors (e.g. position of the vehicle in the queue and gap acceptance) and kinematic factors (e.g. speed and acceleration) on traffic safety. The similarities and differences between this specific AV and MV were identified yielding insight for further developing algorithms for more efficient driving while maintaining the same traffic safety level. For instance, it appears that the AV shows a very conservative left turn-ing behaviour leading to very safe PET distributions in comparison to left turning MV

Online algorithms for multi-level aggregation

In the multilevel aggregation problem (MLAP), requests arrive at the nodes of an edge-weighted tree T and have to be served eventually. A service is defined as a subtree X of T that contains the root of T. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the Transmission Control Protocol acknowledgment problem, whereas for trees of depth 2, it is equivalent to the joint replenishment problem. Aggregation problems for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies, and supply chain management. The instances of MLAP associated with these applications are naturally online, in the sense that aggregation decisions need to be made without information about future requests. Constant-competitive online algorithms are known for MLAP with one or two levels. However, it has been open whether there exist constant-competitive online algorithms for trees of depth more than 2. Addressing this open problem, we give the first constant-competitive online algorithm for trees of arbitrary (fixed) depth. The competitive ratio is O(D42D), where D is the depth of T. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines

New results on multi-level aggregation

International audienceIn the Multi-Level Aggregation Problem (MLAP ), requests for service arrive at the nodes of an edge-weighted rooted tree . Each service is represented by a subtree X of that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs a waiting cost between its arrival and service time. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. The currently best online algorithms for the MLAP achieve competitive ratios polynomial in the tree depth, while the best lower bound is only 3.618. In this paper, we report some progress towards closing this gap, by improving this lower bound and providing several tight bounds for restricted variants of MLAP: (1) We first study a Single-Phase variant of MLAP where all requests are released at the beginning and expire at some unknown time θ, for which we provide an online algorithm with optimal competitive ratio of 4. (2) We prove a lower bound of 4 on the competitive ratio for MLAP, even when the tree is a path. We complement this with a matching upper bound for the deadline variant of MLAP on paths. Additionally, we provide two results for the offline case: (3) We prove that the Single-Phase variant can be solved optimally in polynomial time, and (4) we give a simple 2-approximation algorithm for offline MLAP with deadlines

Super-heavy fermion material as metallic refrigerant for adiabatic demagnetization cooling

Low-temperature refrigeration is of crucial importance in fundamental research of condensed matter physics, as the investigations of fascinating quantum phenomena, such as superconductivity, superfluidity and quantum criticality, often require refrigeration down to very low temperatures. Currently, cryogenic refrigerators with $^3$He gas are widely used for cooling below 1 Kelvin. However, usage of the gas is being increasingly difficult due to the current world-wide shortage. Therefore, it is important to consider alternative methods of refrigeration. Here, we show that a new type of refrigerant, super-heavy electron metal, YbCo$_2$Zn$_{20}$, can be used for adiabatic demagnetization refrigeration, which does not require 3He gas. A number of advantages includes much better metallic thermal conductivity compared to the conventional insulating refrigerants. We also demonstrate that the cooling performance is optimized in Yb$_{1-x}$Sc$_x$Co$_2$Zn$_{20}$ by partial Sc substitution with $x\sim$0.19. The substitution induces chemical pressure which drives the materials close to a zero-field quantum critical point. This leads to an additional enhancement of the magnetocaloric effect in low fields and low temperatures enabling final temperatures well below 100 mK. Such performance has up to now been restricted to insulators. Since nearly a century the same principle of using local magnetic moments has been applied for adiabatic demagnetization cooling. This study opens new possibilities of using itinerant magnetic moments for the cryogen-free refrigeration