On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

Late-Time Convection in the Collapse of a 23 Solar Mass Star

The results of a 3-dimensional SNSPH simulation of the core collapse of a 23 solar mass star are presented. This simulation did not launch an explosion until over 600ms after collapse, allowing an ideal opportunity to study the evolution and structure of the convection below the accretion shock to late times. This late-time convection allows us to study several of the recent claims in the literature about the role of convection: is it dominated by an l=1 mode driven by vortical-acoustic (or other) instability, does it produce strong neutron star kicks, and, finally, is it the key to a new explosion mechanism? The convective region buffets the neutron star, imparting a 150-200 km/s kick. Because the l=1 mode does not dominate the convection, the neutron star does not achieve large (>450 km/s) velocities. Finally, the neutron star in this simulation moves, but does not develop strong oscillations, the energy source for a recently proposed supernova engine. We discuss the implications these results have on supernovae, hypernovae (and gamma-ray bursts), and stellar-massed black holes.Comment: 31 pages (including 13 figures), submitted to Ap

Studies on mouse Moloney virus induced tumours: I. The detection of p30 as a cytotoxic target on murine Moloney leukaemic spleen cells, and on an in vitro Moloney sarcoma line by antibody mediated cytotoxicity.

Antigenic determinants of p30, the most abundant internal virion protein of C type RNA viruses, were detected on the surface of spleen cells from mice bearing Moloney leukaemia and on an in vitro line of Moloney sarcoma, MSC. On both cell types, these determinants on the p30 molecules served as cytotoxic targets in a xenogenic complement dependent antibody mediated 51Cr release assay. Two antisera were used: a rat anti MLV -M induced lymphoma serum, and an antiserum raised in goats to either disrupted FeLV. The cytotoxic target antigens of these antisera were analysed by inhibition of cytotoxicity with viral and cellular proteins

Effect of prolonged space flight on cardiac function and dimensions

Echocardiographic studies were performed preflight 5 days before launch and on recovery day and 1, 2, 4, 11, 31 and 68 days postflight. From these echocardiograms measurements were made. From these primary measurements, left ventricular end-diastolic volume, end-systolic volume, stroke volume, and mass were derived using the accepted assumptions. Findings in the Scientist Pilot and Pilot resemble those seen in trained distance runners. Wall thickness measurements were normal in all three crewmembers preflight. Postflight basal studies were unchanged in the Commander on recovery day through 68 days postflight in both the Scientist Pilot and Pilot, however, the left ventricular end-diastolic volume, stroke volume, and mass were decreased slightly. Left ventricular function curves were constructed for the Commander and Pilot by plotting stroke volume versus end-diastolic volume. In both astronauts, preflight and postflight data fell on the same straight line demonstrating that no deterioration in cardiac function had occurred. These data indicate that the cardiovascular system adapts well to prolonged weightlessness and suggest that alterations in cardiac dimensions and function are unlikely to limit man's future in space

Online bin packing with resource augmentation

In competitive analysis, we usually do not put any restrictions on the computational complexity of online algorithms, although efficient algorithms are preferred. Thus if such an algorithm were given the entire input in advance, it could give an optimal solution (in exponential time). Instead of giving the algorithm more knowledge about the input, in this paper we consider the effects of giving an online bin packing algorithm larger bins than the offline algorithm it is compared to. We give new algorithms for this problem that combine items in bins in an unusual way and give bounds on their performance which improve upon the best possible bounded space algorithm. We also give general lower bounds for this problem which are nearly matching for bin sizes b ?

Lower bounds for on-line single-machine scheduling

The problem of scheduling jobs that arrive over time on a single machine is well-studied. We study the preemptive model and the model with restarts. We provide lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weighted and unweighted total flow time. By using new techniques, we provide the first lower bounds for several of these problems, and we significantly improve the bounds that were known

Minimizing the maximum starting time on-line

We study the scheduling problem of minimizing the maximum starting time on-line. The goal is to minimize the last time that a job starts. We show that while the greedy algorithm has a competitive ratio of $Theta(log m)$, we can give a constant competitive algorithm for this problem. We also show that the greedy algorithm is optimal for resource augmentation in the sense that it requires 2m-1 machines to have a competitive ratio of 1, whereas no algorithm can achieve this with 2m-1 machines

Optimal online bounded space multidimensional packing

We solve an open problem in the literature by providing an online algorithm for multidimensional bin packing that uses only bounded space. We show that it is optimal among bounded space algorithms for any dimension $d>1$. Its asymptotic performance ratio is $(Pi_{infty})^d$, where $Pi_{infty}approx1.691$ is the asymptotic performance ratio of the one-dimensional algorithm harm. A modified version of this algorithm for the case where all items are hypercubes is also shown to be optimal. Its asymptotic performance ratio is sublinear in $d$. Additionally, for the special case of packing squares in two-dimensional bins, we present a new unbounded space online algorithm with asymptotic performance ratio of at most $2.271$. We also present an approximation algorithm for the offline problem with approximation ratio of $16/11$. This improves upon all earlier approximation algorithms for this problem, including the algorithm from Caprara, Packing 2-dimensional bins in harmony, Proc. 43rd FOCS, 2002