Mixed Integer Programming for Searching Maximum Quasi-Bicliques

Filtering Algorithms for the Multiset Ordering Constraint

Constraint programming (CP) has been used with great success to tackle a wide variety of constraint satisfaction problems which are computationally intractable in general. Global constraints are one of the important factors behind the success of CP. In this paper, we study a new global constraint, the multiset ordering constraint, which is shown to be useful in symmetry breaking and searching for leximin optimal solutions in CP. We propose efficient and effective filtering algorithms for propagating this global constraint. We show that the algorithms are sound and complete and we discuss possi…

Markov Chain methods for the bipartite Boolean quadratic programming problem

We study the Bipartite Boolean Quadratic Programming Problem (BBQP) which is an extension of the well known Boolean Quadratic Programming Problem (BQP). Applications of the BBQP include mining discrete patterns from binary data, approximating matrices by rank-one binary matrices, computing the cut-norm of a matrix, and solving optimisation problems such as maximum weight biclique, bipartite maximum weight cut, maximum weight induced sub-graph of a bipartite graph, etc. For the BBQP, we first present several algorithmic components, specifically, hill climbers and mutations, and then show how to…

Satellite downlink scheduling under breakpoint resume mode

A novel problem called satellite downlink scheduling problem (SDSP) under breakpoint resume mode (SDSP-BRM) is studied in our paper. Compared to the traditional SDSP where an imaging data has to be completely downloaded at one time, SDSP-BRM allows the data of an imaging data be broken into a number of pieces which can be downloaded in different playback windows. By analyzing the characteristics of SDSP-BRM, we first propose a mixed integer programming model for its formulation and then prove the NP-hardness of SDSP-BRM. To solve the problem, we design a simple and effective heuristic algorith…

面向抽象结构的更快速对称破缺约束

Faster Symmetry Breaking Constraints for Abstract Structures

针对抽象结构对称破缺时现有方法生成约束多、求解慢的问题，提出一种利用结构表示的不完全对称破缺新方法，在不可区分对象对称场景下速度优于已有方法。

Where the Action is: Let's make Reinforcement Learning for Stochastic Dynamic Vehicle Routing Problems work!

There has been a paradigm-shift in urban logistic services in the last years; demand for real-time, instant mobility and delivery services grows. This poses new challenges to logistic service providers as the underlying stochastic dynamic vehicle routing problems (SDVRPs) require anticipatory real-time routing actions. Searching the combinatorial action space for efficient routing actions is by itself a complex task of mixed-integer programming (MIP) well-known by the operations research community. This complexity is now multiplied by the challenge of evaluating such actions with respect to th…

Sequence Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations

Unbalanced translocations are among the most frequent chromosomal alterations, accounted for 30\% of all losses of heterozygosity, a major genetic event causing inactivation of tumor suppressor genes. Despite of their central role in genomic sequence analysis, little attention has been devoted to the problem of matching sequences allowing for this kind of chromosomal alteration. In this paper we investigate the \emph{approximate string matching} problem when the edit operations are non-overlapping unbalanced translocations of adjacent factors. In particular, we first present a $O(nm^3)$-time a…

On the Complexity of Searching in Trees: Average-case Minimization

We focus on the average-case analysis: A function w : V -> Z+ is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper, very little was known about this natural question and the complexity of the problem had remained so far an open question. We close this question and prove that the above tree search problem is NP-complete even for the class of trees with diameter at most 4. This results in a complete characterization of the complexity of the problem with respect to the diameter size. In f…

一种用于存储和搜索最大公共子序列的紧凑有向无环图（DAG）

A Compact DAG for Storing and Searching Maximal Common Subsequences

本研究针对最大公共子序列（MCSs）紧凑表示的复杂度难题，提出多项式时间构造多项式规模DAG的方法，支持MCSs的高效枚举、计数与随机访问，填补了MCSs与LCSs间的复杂度差距，为新型序列分析奠定基础。

Text Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations

In this paper we investigate the \emph{approximate string matching problem} when the allowed edit operations are \emph{non-overlapping unbalanced translocations of adjacent factors}. Such kind of edit operations take place when two adjacent sub-strings of the text swap, resulting in a modified string. The two involved substrings are allowed to be of different lengths. Such large-scale modifications on strings have various applications. They are among the most frequent chromosomal alterations, accounted for 30\% of all losses of heterozygosity, a major genetic event causing inactivation of canc…

Evaluating and Tuning n-fold Integer Programming

In recent years, algorithmic breakthroughs in stringology, computational social choice, scheduling, etc., were achieved by applying the theory of so-called $n$-fold integer programming. An $n$-fold integer program (IP) has a highly uniform block structured constraint matrix. Hemmecke, Onn, and Romanchuk [Math. Programming, 2013] showed an algorithm with runtime $a^{O(rst + r^2s)} n^3$, where $a$ is the largest coefficient, $r,s$, and $t$ are dimensions of blocks of the constraint matrix and $n$ is the total dimension of the IP; thus, an algorithm efficient if the blocks are of small size and w…

Finding Triangles and Other Small Subgraphs in Geometric Intersection Graphs

We consider problems related to finding short cycles, small cliques, small independent sets, and small subgraphs in geometric intersection graphs. We obtain a plethora of new results. For example: * For the intersection graph of $n$ line segments in the plane, we give algorithms to find a 3-cycle in $O(n^{1.408})$ time, a size-3 independent set in $O(n^{1.652})$ time, a 4-clique in near-$O(n^{24/13})$ time, and a $k$-clique (or any $k$-vertex induced subgraph) in $O(n^{0.565k+O(1)})$ time for any constant $k$; we can also compute the girth in near-$O(n^{3/2})$ time. * For the intersection grap…