ILP Solution Research Articles

Recombinations, chains and caps: resolving problems with the DCJ-indel model

One of the most fundamental problems in genome rearrangement studies is the (genomic) distance problem. It is typically formulated as finding the minimum number of rearrangements under a model that are needed to transform one genome into the other. A powerful multi-chromosomal model is the Double Cut and Join (DCJ) model.While the DCJ model is not able to deal with some situations that occur in practice, like duplicated or lost regions, it was extended over time to handle these cases. First, it was extended to the DCJ-indel model, solving the issue of lost markers. Later ILP-solutions for so called natural genomes, in which each genomic region may occur an arbitrary number of times, were developed, enabling in theory to solve the distance problem for any pair of genomes. However, some theoretical and practical issues remained unsolved. On the theoretical side of things, there exist two disparate views of the DCJ-indel model, motivated in the same way, but with different conceptualizations that could not be reconciled so far. On the practical side, while ILP solutions for natural genomes typically perform well on telomere to telomere resolved genomes, they have been shown in recent years to quickly loose performance on genomes with a large number of contigs or linear chromosomes. This has been linked to a particular technique, namely capping. Simply put, capping circularizes linear chromosomes by concatenating them during solving time, increasing the solution space of the ILP superexponentially. Recently, we introduced a new conceptualization of the DCJ-indel model within the context of another rearrangement problem. In this manuscript, we will apply this new conceptualization to the distance problem. In doing this, we uncover the relation between the disparate conceptualizations of the DCJ-indel model. We are also able to derive an ILP solution to the distance problem that does not rely on capping. This solution significantly improves upon the performance of previous solutions on genomes with high numbers of contigs while still solving the problem exactly and being competitive in performance otherwise. We demonstrate the performance advantage on simulated genomes as well as showing its practical usefulness in an analysis of 11 Drosophila genomes.

Virtual Network Function Service Provisioning in MEC Via Trading Off the Usages Between Computing and Communication Resources

Mobile edge computing (MEC) has emerged as a promising technology that offers resource-intensive yet delay-sensitive applications from the edge of mobile networks. With the emergence of complicated and resource-hungry mobile applications, offloading user tasks to cloudlets of nearby mobile edge-cloud networks is becoming an important approach to leverage the processing capability of mobile devices, reduce mobile device energy consumptions, and improve experiences of mobile users. In this article we first study the provisioning of virtualized network function (VNF) services for user requests in an MEC network, where each user request has a demanded data packet rate with a specified network function service requirement, and different user requests need different services that are represented by virtualized network functions instantiated in cloudlets. We aim to maximize the number of user request admissions while minimizing their admission cost, where the request admission cost consists of the computing cost on instantiations of requested VNF instances and the data packet traffic processing of requests in their VNF instances, and the communication cost of routing data packet traffic of requests between users and the cloudlets hosting their requested VNF instances. We study the joint VNF instance deployment and user requests assignment in MEC, by explicitly exploring a non-trivial usage tradeoff between different types of resources. To this end, we first formulate the cost minimization problem that admits all requests by assuming that there is sufficient computing resource in MEC to accommodate the requested VNF instances of all requests, for which we formulate an Integer Linear Programming solution and two efficient heuristic algorithms. We then deal with the problem under the computing resource constraint. We term this problem as the throughput maximization problem by admitting as many as requests, subject to computing resource capacity on each cloudlet, for which we formulate an ILP solution when the problem size is small; otherwise, we devise efficient algorithms for it. We finally evaluate the performance of the proposed algorithms through experimental simulations. Experimental results demonstrate that the proposed algorithms are promising. To the best of our knowledge, we are the first to explicitly explore the usage tradeoff between computing and communication resources in the admissions of user requests in MEC through introducing a novel load factor concept to minimize the request admission cost and maximize the network throughput.

Limiting the memory footprint when dynamically scheduling DAGs on shared-memory platforms

Scientific workflows are frequently modeled as Directed Acyclic Graphs (DAGs) of tasks, which represent computational modules and their dependences in the form of data produced by a task and used by another one. This formulation allows the use of runtime systems which dynamically allocate tasks onto the resources of increasingly complex computing platforms. However, for some workflows, such a dynamic schedule may run out of memory by processing too many tasks simultaneously. This paper focuses on the problem of transforming such a DAG to prevent memory shortage, and concentrates on shared memory platforms. We first propose a simple model of DAGs which is expressive enough to emulate complex memory behaviors. We then exhibit a polynomial-time algorithm that computes the maximum peak memory of a DAG, that is, the maximum memory needed by any parallel schedule. We consider the problem of reducing this maximum peak memory to make it smaller than a given bound. Our solution consists in adding new fictitious edges, while trying to minimize the critical path of the graph. After proving that this problem is NP-complete, we provide an ILP solution as well as several heuristic strategies that are thoroughly compared by simulation on synthetic DAGs modeling actual computational workflows. We show that on most instances we are able to decrease the maximum peak memory at the cost of a small increase in the critical path, thus with little impact on the quality of the final parallel schedule.

Optimization algorithms for transmission range and actor movement in wireless sensor and actor networks

Wireless sensor and actor networks are composed of static sensors and mobile actors. We assume actors have a random initial location in the two-dimensional sensing area. The objective is to move each actor to a location such that every sensor node is within a bounded number of hops from some actor. Because sensors have limited energy, the new actor locations are chosen to minimize the transmission range of the sensors. However, actors also have a limited (although larger) power supply, and their movement depletes their resources. It follows that by carefully choosing the new actor locations, the total actor movement can be minimized. In this paper, we introduce the problem of simultaneously minimizing the required transmission range and amount of actor movement. To find a solution, we formulate the problem using an ILP framework. For the ILP solution to be feasible, we introduce a finite set of possible actor locations such that an optimal solution is guaranteed to be found within this set. We also present a heuristic for this problem. As a preliminary step, we study minimizing the transmission range necessary for multi-hop communication. Various heuristics for this smaller problem are proposed and their results are compared by simulation. The best of these heuristics is then enhanced to incorporate minimizing the movement of actors, and its performance is compared to the optimal ILP solution.

Freezing forwarding functionality to make the network greener

This work proposes a novel approach to reduce the power consumption of IP routers: freezing the forwarding engine of routers line-cards. In fact, recent studies showed that about 60% of the power consumption of a line-card is wasted to lookup the routing table during packet forwarding process. We first define the proposed approach, called Freezing Forwarding Functionality (F3). Then, we provide an ILP formulation of the energy minimization problem under F3mode and define a heuristic algorithm, referred to as Green Backbone Algorithm (GBA), to solve the problem in large networks. The performance of GBA is evaluated under different traffic scenarios in real ISP network topologies, and a comparison with the ILP solution is carried out for small networks. Results show that: (i) GBA performance, in terms of number of nodes in F3mode, are very close to optimal ILP solution ones; (ii) a large energy saving (up to 80% of nodes in F3mode ) is obtained in large networks during low traffic hours; (iii) a limited impact on paths length increase is achieved.

Automated bond order assignment as an optimization problem

Numerous applications in Computational Biology process molecular structures and hence strongly rely not only on correct atomic coordinates but also on correct bond order information. For proteins and nucleic acids, bond orders can be easily deduced but this does not hold for other types of molecules like ligands. For ligands, bond order information is not always provided in molecular databases and thus a variety of approaches tackling this problem have been developed. In this work, we extend an ansatz proposed by Wang et al. that assigns connectivity-based penalty scores and tries to heuristically approximate its optimum. In this work, we present three efficient and exact solvers for the problem replacing the heuristic approximation scheme of the original approach: an A*, an ILP and an fixed-parameter approach (FPT) approach. We implemented and evaluated the original implementation, our A*, ILP and FPT formulation on the MMFF94 validation suite and the KEGG Drug database. We show the benefit of computing exact solutions of the penalty minimization problem and the additional gain when computing all optimal (or even suboptimal) solutions. We close with a detailed comparison of our methods. The A* and ILP solution are integrated into the open-source C++ LGPL library BALL and the molecular visualization and modelling tool BALLView and can be downloaded from our homepage www.ball-project.org. The FPT implementation can be downloaded from http://bio.informatik.uni-jena.de/software/.

Tackling group-to-tree matching in large scale group communications

As a mechanism to efficiently support group communications, multicasting, faces a serious state scalability problem when there are large numbers of groups in the network. Recently, a novel solution called Aggregated Multicast has been proposed, in which multiple groups can share one delivery tree. A key problem in Aggregated Multicast is group-to-tree matching (i.e., assigning groups to proper trees). In this paper, we formally define this problem, and formulate two versions of the problem: static and dynamic. We analyze the static version and prove that it is NP-complete. To tackle this hard problem, we propose three algorithms: one optimal (using Linear Integer Programming, or ILP), one near-optimal (using Greedy method), and one Pseudo-Dynamic algorithm. For the dynamic version, we present a generic dynamic on-line algorithm. Simulation study has been conducted to evaluate the performance of the algorithms. Our results show that: (1) for the static problem, the Greedy algorithm is a feasible solution and its performance is very close to the optimal ILP solution, while the Pseudo-Dynamic algorithm is a good heuristic for many cases where Greedy does not work well; (2) for the dynamic problem, the generic dynamic on-line algorithm is a very practical solution with promising performance and reasonable computation requirement.