CG:SHOP is an annual geometric optimization challenge and the 2022 edition proposed the problem of coloring a certain geometric graph defined by line segments. Surprisingly, the top three teams used the same technique, called conflict optimization. This technique has been introduced in the 2021 edition of the challenge, to solve a coordinated motion planning problem. In this paper, we present the technique in the more general framework of binary constraint satisfaction problems (binary CSP). Then, the top three teams describe their different implementations of the same underlying strategy. We evaluate the performance of those implementations to vertex color not only geometric graphs, but also other types of graphs.
Over the last decades, new mobility offers have emerged to enlarge the coverage and the accessibility of public transportation systems. In many areas, public transit now incorporates on-demand transport lines, that can be activated at user need. In this paper, we propose to integrate lines without predefined schedules but with predefined stop sequences into a state-of-the-art trip planning algorithm for public transit, the Trip-Based Public Transit Routing algorithm [ 33 ]. We extend this algorithm to non-scheduled lines and explain how to model other modes of transportation, such as bike sharing, with this approach. The resulting algorithm is exact and optimizes two criteria: the earliest arrival time and the minimal number of transfers. Experiments on two large datasets show the interest of the proposed method over a baseline modelling.
One way to solve very large linear programs in standard form is to apply a random projection to the constraints, then solve the projected linear program [ 63 ]. This will yield a guaranteed bound on the optimal value, as well as a solution to the projected linear program. The process of constructing an approximate solution of the original linear program is called solution retrieval. We improve theoretical bounds on the approximation error of the retrieved solution obtained as in Reference [ 42 ] and propose an improved retrieval method based on alternating projections. We show empirical results illustrating the practical benefits of the new approach.
In this paper we study a fingerprint-based minimal perfect hash function ( FMPH for short). While FMPH is not as space-efficient as some other minimal perfect hash functions (for example RecSplit, CHD, or PTHash), it has a number of practical advantages that make it worthy of consideration. FMPH is simple and quite fast to evaluate. Its construction requires very little auxiliary memory, takes a short time and, in addition, can be parallelized or carried out without holding keys in memory. In this paper, we propose an effective method (called FMPHGO ) that reduces the size of FMPH, as well as a number of implementation improvements. In addition, we experimentally study FMPHGO performance and find the best values for its parameters. Our benchmarks show that with our method and an efficient structure to support the rank queries on a bit vector, the FMPH size can be reduced to about 2.1 bits/key, which is close to the size achieved by state-of-the-art methods and noticeably larger only compared to RecSplit. FMPHGO preserves most of the FMPH advantages mentioned above, but significantly reduces its construction speed. However, FMPHGO’s construction speed is still competitive with methods of similar space efficiency (like CHD or PTHash), and seems to be good enough for practical applications.
The uniform capacitated vertex k -center problem is an 𝒩𝒫 -hard combinatorial optimization problem that models real situations where k centers can only attend a maximum number of customers, and the travel time or distance from the customers to their assigned center has to be minimized. This article introduces a polynomial-time constructive heuristic algorithm that exploits the relationship between this problem and the minimum capacitated dominating set problem. The proposed heuristic is based on the one-hop farthest-first heuristic that has proven effective for the uncapacitated version of the problem. We carried out different empirical evaluations of the proposed heuristic, including an analysis of the effect of a parallel implementation of the algorithm, which significantly improved the running time for relatively large instances.
