The interval constrained 3-coloring problem

In this paper, we settle the open complexity status of interval constrained coloring with a fixed number of colors. We prove that the problem is already NP-complete if the number of different colors is 3. Previously, it has only been known that it is NP-complete, if the number of colors is part of the input and that the problem is solvable in polynomial time, if the number of colors is at most 2. We also show that it is hard to satisfy almost all of the constraints for a feasible instance.Comment: minor revisio

Lossless and near-lossless source coding for multiple access networks

A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of correlated information sequences {X-i}(i=1)(infinity), and {Y-i}(i=1)(infinity) is drawn independent and identically distributed (i.i.d.) according to joint probability mass function (p.m.f.) p(x, y); the encoder for each source operates without knowledge of the other source; the decoder jointly decodes the encoded bit streams from both sources. The work of Slepian and Wolf describes all rates achievable by MASCs of infinite coding dimension (n --> infinity) and asymptotically negligible error probabilities (P-e((n)) --> 0). In this paper, we consider the properties of optimal instantaneous MASCs with finite coding dimension (n 0) performance. The interest in near-lossless codes is inspired by the discontinuity in the limiting rate region at P-e((n)) = 0 and the resulting performance benefits achievable by using near-lossless MASCs as entropy codes within lossy MASCs. Our central results include generalizations of Huffman and arithmetic codes to the MASC framework for arbitrary p(x, y), n, and P-e((n)) and polynomial-time design algorithms that approximate these optimal solutions

Algorithms for the minimum sum coloring problem: a review

The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex coloring problem which has a number of AI related applications. Due to its theoretical and practical relevance, MSCP attracts increasing attention. The only existing review on the problem dates back to 2004 and mainly covers the history of MSCP and theoretical developments on specific graphs. In recent years, the field has witnessed significant progresses on approximation algorithms and practical solution algorithms. The purpose of this review is to provide a comprehensive inspection of the most recent and representative MSCP algorithms. To be informative, we identify the general framework followed by practical solution algorithms and the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the reviewed methods, we wish to encourage future development of more powerful methods and motivate new applications

On the Complexity of Spill Everywhere under SSA Form

Compilation for embedded processors can be either aggressive (time consuming cross-compilation) or just in time (embedded and usually dynamic). The heuristics used in dynamic compilation are highly constrained by limited resources, time and memory in particular. Recent results on the SSA form open promising directions for the design of new register allocation heuristics for embedded systems and especially for embedded compilation. In particular, heuristics based on tree scan with two separated phases -- one for spilling, then one for coloring/coalescing -- seem good candidates for designing memory-friendly, fast, and competitive register allocators. Still, also because of the side effect on power consumption, the minimization of loads and stores overhead (spilling problem) is an important issue. This paper provides an exhaustive study of the complexity of the ``spill everywhere'' problem in the context of the SSA form. Unfortunately, conversely to our initial hopes, many of the questions we raised lead to NP-completeness results. We identify some polynomial cases but that are impractical in JIT context. Nevertheless, they can give hints to simplify formulations for the design of aggressive allocators.Comment: 10 page

Control and Synchronization of Neuron Ensembles

Synchronization of oscillations is a phenomenon prevalent in natural, social, and engineering systems. Controlling synchronization of oscillating systems is motivated by a wide range of applications from neurological treatment of Parkinson's disease to the design of neurocomputers. In this article, we study the control of an ensemble of uncoupled neuron oscillators described by phase models. We examine controllability of such a neuron ensemble for various phase models and, furthermore, study the related optimal control problems. In particular, by employing Pontryagin's maximum principle, we analytically derive optimal controls for spiking single- and two-neuron systems, and analyze the applicability of the latter to an ensemble system. Finally, we present a robust computational method for optimal control of spiking neurons based on pseudospectral approximations. The methodology developed here is universal to the control of general nonlinear phase oscillators.Comment: 29 pages, 6 figure

Population stability: regulating size in the presence of an adversary

We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size $N$. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and $\omega(\log^2 N)$ states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size

MARACAS: a real-time multicore VCPU scheduling framework

This paper describes a multicore scheduling and load-balancing framework called MARACAS, to address shared cache and memory bus contention. It builds upon prior work centered around the concept of virtual CPU (VCPU) scheduling. Threads are associated with VCPUs that have periodically replenished time budgets. VCPUs are guaranteed to receive their periodic budgets even if they are migrated between cores. A load balancing algorithm ensures VCPUs are mapped to cores to fairly distribute surplus CPU cycles, after ensuring VCPU timing guarantees. MARACAS uses surplus cycles to throttle the execution of threads running on specific cores when memory contention exceeds a certain threshold. This enables threads on other cores to make better progress without interference from co-runners. Our scheduling framework features a novel memory-aware scheduling approach that uses performance counters to derive an average memory request latency. We show that latency-based memory throttling is more effective than rate-based memory access control in reducing bus contention. MARACAS also supports cache-aware scheduling and migration using page recoloring to improve performance isolation amongst VCPUs. Experiments show how MARACAS reduces multicore resource contention, leading to improved task progress.http://www.cs.bu.edu/fac/richwest/papers/rtss_2016.pdfAccepted manuscrip