Optimizing the application order under precedent-based decision-making

With the rapid growth of Internet, plenty of applications has been implemented for users to exchange resources with each other over networks. As a result, it has been a critical challenge to efficiently and fairly allocate resource among participating agents. Motivated by the famous BitTorrent system, a BD Mechanism for resource exchange allocation is proposed, which is based on a combinatorial structure called bottleneck decomposition. The mechanism has been shown to lead to market equilibrium, a state optimizing each individual's utility, and to be truthful, that is robust against agents' strategic behaviors. However, the crux on how to compute a bottleneck decomposition of any graph remains untouched. In this paper, we focus on the computation of bottleneck decomposition to fill the blanks and prove that the bottleneck decomposition of a network can be computed in O(n^6\log(nU)) time, where n and U are the number of agents and the maximal amount of resource any agent has in the network. Based on the bottleneck decomposition, a fair allocation in a resource exchange network can be obtained in polynomial time. We further carefully discuss the fairness in resource exchange scenario, showing the derived allocation satisfies several common fairness notions simultaneously.

In order to satisfy the capability generation requirement of command information system, a load balancing method for service scheduling is studied. Considering that a work which will be finished by command information system based on service-oriented architecture is composed of several jobs, the paper analyzes the work completion process in detail. Then, a method to measure the load on a service which is scheduled to participate in a work is designed. On that basis, a load balancing mathematical model for service scheduling is established and a model solving algorithm that is based on greedy strategy and has polynomial time is put forward. Simulated experimental results show that the method proposed in this paper can allocate load to the services of command information system in a balanced way.

We propose a distance between continuous-time Markov chains (CTMCs) and study the problem of computing it by comparing three different algorithmic methodologies: iterative, linear program, and on-the-fly. In a work presented at FoSSaCS'12, Chen et al. characterized the bisimilarity distance of Desharnais et al. between discrete-time Markov chains as an optimal solution of a linear program that can be solved by using the ellipsoid method. Inspired by their result, we propose a novel linear program characterization to compute the distance in the continuous-time setting. Differently from previous proposals, ours has a number of constraints that is bounded by a polynomial in the size of the CTMC. This, in particular, proves that the distance we propose can be computed in polynomial time. Despite its theoretical importance, the proposed linear program characterization turns out to be inefficient in practice. Nevertheless, driven by the encouraging results of our previous work presented at TACAS'13, we propose an efficient on-the-fly algorithm, which, unlike the other mentioned solutions, computes the distances between two given states avoiding an exhaustive exploration of the state space. This technique works by successively refining over-approximations of the target distances using a greedy strategy, which ensures that the state space is further explored only when the current approximations are improved. Tests performed on a consistent set of (pseudo)randomly generated CTMCs show that our algorithm improves, on average, the efficiency of the corresponding iterative and linear program methods with orders of magnitude.

We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different algorithmic techniques: (1) a rounding technique tailored to a convex relaxation in conjunction with a non-convex relaxation whose approximation ratio equals the golden ratio; (2) a greedy strategy; (3) a randomized rounding method leading to an approximation algorithm for the more general case with multiple convex quadratic constraints. We further show that a combination of the first two strategies can be used to yield a monotone algorithm leading to a strategyproof mechanism for a game-theoretic variant of the problem. Finally, we present a computational study of the empirical approximation of the three algorithms for problem instances arising in the context of real-world gas transport networks.

LP-Based Approaches to Stationary-Constrained Markov Decision Problems

Several implicit methods to infer horizontal gene transfer (HGT) focus on pairs of genes that have diverged only after the divergence of the two species in which the genes reside. This situation defines the edge set of a graph, the later-divergence-time (LDT) graph, whose vertices correspond to genes colored by their species. We investigate these graphs in the setting of relaxed scenarios, i.e., evolutionary scenarios that encompass all commonly used variants of duplication-transfer-loss scenarios in the literature. We characterize LDT graphs as a subclass of properly vertex-colored cographs, and provide a polynomial-time recognition algorithm as well as an algorithm to construct a relaxed scenario that explains a given LDT. An edge in an LDT graph implies that the two corresponding genes are separated by at least one HGT event. The converse is not true, however. We show that the complete xenology relation is described by an rs-Fitch graph, i.e., a complete multipartite graph satisfying constraints on the vertex coloring. This class of vertex-colored graphs is also recognizable in polynomial time. We finally address the question “how much information about all HGT events is contained in LDT graphs” with the help of simulations of evolutionary scenarios with a wide range of duplication, loss, and HGT events. In particular, we show that a simple greedy graph editing scheme can be used to efficiently detect HGT events that are implicitly contained in LDT graphs.

We study stable matching problems in networks where players are embedded in a social context, and may incorporate friendship relations or altruism into their decisions. Each player is a node in a social network and strives to form a good match with a neighboring player. We consider the existence, computation, and inefficiency of stable matchings from which no pair of players wants to deviate. When the benefits from a match are the same for both players, we show that incorporating the well-being of other players into their matching decisions significantly decreases the price of stability, while the price of anarchy remains unaffected. Furthermore, a good stable matching achieving the price of stability bound always exists and can be reached in polynomial time. We extend these results to more general matching rewards, when players matched to each other may receive different utilities from the match. For this more general case, we show that incorporating social context (i.e., “caring about your friends”) can make an even larger difference, and greatly reduce the price of anarchy. We show a variety of existence results, and present upper and lower bounds on the prices of anarchy and stability for various matching utility structures.

It is well known that a search engine can significantly benefit from an auxiliary database, which can suggest interpretations of the search query by means of the involved concepts and their interrelationship. The difficulty is to translate abstract notions like concept and interpretation into a concrete search algorithm that operates over the auxiliary database. To surpass existing heuristics, there is a need for a formal basis, which is realized in this paper through the framework of a search database system, where an interpretation is identified as a parse. It is shown that the parses of a query can be generated in polynomial time in the combined size of the input and the output, even if parses are restricted to those having a nonempty evaluation. Identifying that one parse is more specific than another is important for ranking answers, and this framework captures the precise semantics of being more specific; moreover, performing this comparison between parses is tractable. Lastly, the paper studies the problem of finding the most specific parses. Unfortunately, this problem turns out to be intractable in the general case. However, under reasonable assumptions, the parses can be enumerated in an order of decreasing specificity, with polynomial delay and polynomial space.

In this paper, we show that checking some properties of Boolean functions which are given by the lists of monomials in their polynomial representations can be implemented in polynomial time. Multi-linear polynomials over GF(2) are often a convenient way to represent Boolean functions. There is a single polynomial for each Boolean function, and the length of the polynomial (i.e. the number of its monomials) which represents a function of n variables can be far less than 2n. Therefore, in some cases, polynomials are a compressed description of Boolean functions. Besides, polynomial representations of Boolean functions have applications in circuit lower bounds, computational learning, error-correcting codes, cryptography. We construct polynomial-time algorithms for checking some properties of Boolean functions which are given by the lists of monomials in their polynomial representations. The considered properties are self-anti-duality (evenness), self-duality, periodicity, 1-invariance (Mobius transform invariance, coincidence). Note that checking each of these properties directly by definition gives, in the general case, only exponential-time algorithms. The approach to construct our algorithms is the following. Firstly, we prove that if a Boolean function has a certain property then its polynomial has a special structure. And secondly, we check the property by its characterization, cutting negative cases by proven facts. More precisely, we analyze an exponential time algorithm and prove that if the number of steps of the algorithm exceeds a bound, which is polynomial in the input size, and may be computed in advance, then the input will be necessarily rejected.

The complexity of manipulative attacks in nearly single-peaked electorates

Probabilistic circuits are a class of probabilistic generative models that allow us to compute different types of probabilistic queries in polynomial time. Unlike many of the mainstream approaches for generative modeling, they can compute exact likelihoods, marginals, and expectations. Yet, assessing the reliability of their inferences is not straightforward. Credal probabilistic circuits are the imprecise counterpart of probabilistic circuits allowing, among other queries, computations of cautious inferences and sensitivity analyses. In this work, we propose an efficient algorithm to compute the lower and upper expectations for factorizing functions using a credal probabilistic circuit. We discuss under what structural assumptions and types of factorizing functions the algorithm works. We prove that such algorithm has polynomial time complexity in the input size. In the general case, we prove that computing cautious inferences using credal probabilistic circuits is an NP-hard problem, yet the proposed algorithm can be used as an approximation. Some experiments show how the approximation degrades with the complexity of the model structure.

Optimal schedule for works running on machines, in a general case, is a hard problem and there is no complete optimal deterministic algorithm in polynomial time. Optimal and approximated solutions were issued for some specific cases with constraints. One can find the solutions for the cases 1 and 2 machines [4,16] as the initial algorithms. In [16], author solved late works problem using algorithm with setup times included. [4] solve the due works problem on two machines, and can be extended for the case of 3 machines with some conditions on works. Other authors looked at schedule problems in specific cases like [5,8,17]. In this paper, we apply duration automata [1,2] to solve the schedule problem dynamically for the works with uncertain processing time in a cluster computer, which is a system consisting of many computers (computing nodes) co-working together. We solve the schedule problem in a cluster with $m$ machines for two cases: all machines are the same and different in configurations (machine's resources are formally considered as a configuration information, represented by the time need to finish the works). Because of uncertainly processing time, tranditional algorithms can not be used effectively. By using DA model with DA's order criterion, we issue schedule algorithms and practically prove to be better in time consuming compare to FIFO (natural order), the fastest first (greedy) and the longest first (safety) methods without synchronized points.

This paper considers a model of a hierarchical system of the Principal–agent type, in which the Principal manages the set of agent’s choices. The model of such a system is a hierarchical two-player game with forbidden situations. In this game, the Principal chooses some subset of a fixed set, whereas the agent chooses his control from this subset. The agent’s payoff explicitly depends on his own choice only, whereas the Principal’s payoff depends both on the agent’s control and on its own choice. The dependence of the Principal’s payoff on his choice is assumed to be monotonic with respect to the inclusion relation on the set of his strategies. The problems formulated below are to calculate the Principal’s maximum guaranteed result, under the assumption of the agent’s benevolence and without this assumption. A new definition of the Principal’s maximum guaranteed result in the game with a benevolent agent is proposed, which remains correct also in the case when the agent’s payoff achieves no maximum for some of the Principal’s strategies. The equivalence of this definition to the classical Stackelberg’s definition is proved for the cases in which the latter is correct. In the general case, the problems formulated below require calculating the maximin with bound constraints on complex infinite-dimensional spaces. Some methods for simplifying these problems are suggested. In the case of a finite basic set, algorithms for solving the problem in a polynomial time with respect to the number of elements in this set are developed. In the case of infinite basic set, the problem is reduced to a sequence of ordinary optimization problems. The methods proposed below can be used to construct and investigate many applications-relevant models of this type.

This paper addresses a one-machine scheduling problem in which the efficiency of the machine is not constant, that is the duration of a task is longer in badly efficient time periods. Each task has an irregular completion cost. Under the assumption that the efficiency constraints are time-periodic, we show that the special case where the sequence is fixed can be solved in polynomial time. The general case is NP-complete so that we propose a two-phase heuristic to find good solutions. Our approach is tested on problems with earliness-tardiness costs.

We introduce an exponential neighborhood for the Vehicle Routing Problem (vrp) with unit customers’ demands, and we show that it can be explored efficiently in polynomial time by reducing its exploration to a particular case of the Restricted Complete Matching (rcm) problem that we prove to be polynomial time solvable using flow techniques. Furthermore, we show that in the general case with non-unit customers’ demands the exploration of the neighborhood becomes an \(\mathcal{NP}\) -hard problem.